作者机构：
[Liu, Hui-qing; Zhang, Rui-ting] Hubei Univ, Hubei Key Lab Appl Math, Wuhan 430062, Peoples R China.;[Liu, Hui-qing; Zhang, Rui-ting] Hubei Univ, Fac Math & Stat, Wuhan 430062, Peoples R China.;[Hu, Xiao-lan] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Hu, Xiao-lan] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Hu, XL ] C;Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
摘要：
Motivated by a discrete-time process intended to measure the speed of the spread of contagion in a graph, the burning number b(G) of a graph G, is defined as the smallest integer k for which there are vertices x(1),& mldr;,x(k) such that for every vertex u of G, there exists i is an element of {1,& mldr;,k} with d(G)(u, x(i)) <= k - i, and d(G)(x(i), x(j)) >= j - i for any 1 <= i < j <= k. The graph burning problem has been shown to be NP-complete even for some acyclic graphs with maximum degree three. In this paper, we determine the burning numbers of all short barbells and long barbells, respectively.
作者机构：
[Bao, Kangbo] School of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, PR China. Electronic address: baokangbo@163.com;[Liang, Guizhen] School of Mathematics and Information Science, Xinxiang University, Xinxiang, 453003, PR China. Electronic address: lgz3361@163.com;[Tian, Tianhai] School of Mathematics, Monash University, Melbourne, VIC 3800, Australia. Electronic address: tianhai.tian@monash.edu;[Zhang, Xinan] School of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, PR China. Electronic address: xinanzhang@mail.ccnu.edu.cn
通讯机构：
[Zhang, Xinan; Tian, Tianhai; Bao, Kangbo; Liang, Guizhen] S;School of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, PR China. Electronic address:;School of Mathematics and Information Science, Xinxiang University, Xinxiang, 453003, PR China. Electronic address:;School of Mathematics, Monash University, Melbourne, VIC 3800, Australia. Electronic address: tianhai.
关键词：
Drug resistance;Global stability;Immunotherapy;Mathematical model;Targeted therapy
摘要：
Drug resistance is one of the most intractable issues to the targeted therapy for cancer diseases. To explore effective combination therapy schemes, we propose a mathematical model to study the effects of different treatment schemes on the dynamics of cancer cells. Then we characterize the dynamical behavior of the model by finding the equilibrium points and exploring their local stability. Lyapunov functions are constructed to investigate the global asymptotic stability of the model equilibria. Numerical simulations are carried out to verify the stability of equilibria and treatment outcomes using a set of collected model parameters and experimental data on murine colon carcinoma. Simulation results suggest that immunotherapy combined with chemotherapy contributes significantly to the control of tumor growth compared to monotherapy. Sensitivity analysis is performed to identify the importance of model parameters on the variations of model outcomes.
作者机构：
[Xiang, Jianli] China Three Gorges Univ, Three Gorges Math Res Ctr, Yichang 443002, Peoples R China.;[Yan, Guozheng; Yan, GZ] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Yan, GZ ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
摘要：
We consider the interior transmission eigenvalue problem corresponding to the scattering for an anisotropic medium of the scalar Helmholtz equation in the case where the boundary partial differential omega is split into two disjoint parts and possesses different transmission conditions. Using the variational method, we obtain the well posedness of the interior transmission problem, which plays an important role in the proof of the discreteness of eigenvalues. Then we achieve the existence of an infinite discrete set of transmission eigenvalues provided that n equivalent to 1, where a fourth order differential operator is applied. In the case of n not equivalent to 1, we show the discreteness of the transmission eigenvalues under restrictive assumptions by the analytic Fredholm theory and the T-coercive method.
期刊：
Journal of Mathematical Physics,2024年65(2):021503 ISSN：0022-2488
通讯作者：
Zhang, J
作者机构：
[Zhang, Jing; Lei, Yuanjie; Zhang, J] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan, Peoples R China.;[Zhang, Xueying] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.
通讯机构：
[Zhang, J ] H;Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan, Peoples R China.
摘要：
In this paper, we establish the existence of small-amplitude unique solutions near the Maxwellian for the Fokker-Planck-Boltzmann equation in a finite channel with specular reflection boundary conditions. The solution space we consider is denoted as Lk1LT infinity Lx1,v2, introduced in Duan et al. [Commun. Pure Appl. Math. 74(5), 932-1020 (2021)]. In addition, we investigate the long-time behavior of solutions for both hard and soft potentials.
期刊：
JOURNAL OF ALGEBRA AND ITS APPLICATIONS,2024年 ISSN：0219-4988
通讯作者：
Shu, B
作者机构：
[Chang, Hao] Cent China Normal Univ, Sch Math & Stat, 152 Luoyu Rd, Wuhan 430079, Peoples R China.;[Chang, Hao] Cent China Normal Univ, Hubei Key Lab Math Sci, 152 Luoyu Rd, Wuhan, Peoples R China.;[Shu, Bin] East China Normal Univ, Sch Math Sci, Key Lab Math & Engn Applicat, Minist Educ, 500 Dongchuan Rd, Shanghai 200241, Peoples R China.;[Shu, Bin] East China Normal Univ, Shanghai Key Lab PMMP, 500 Dongchuan Rd, Shanghai 200241, Peoples R China.;[Yao, Yu-Feng] Shanghai Maritime Univ, Dept Math, 1550 Haigang Ave, Shanghai 201306, Peoples R China.
通讯机构：
[Shu, B ] E;East China Normal Univ, Sch Math Sci, Key Lab Math & Engn Applicat, Minist Educ, 500 Dongchuan Rd, Shanghai 200241, Peoples R China.;East China Normal Univ, Shanghai Key Lab PMMP, 500 Dongchuan Rd, Shanghai 200241, Peoples R China.
摘要：
In this note, we investigate Jacobian conjecture through investigation of automorphisms of polynomial rings in characteristic p. Making use of the technique of inverse limits, we show that under Jacobian condition for a given homomorphism phi of the polynomial ring k[x(1),& sdot;& sdot;& sdot;, x(n)], if phi preserves the maximal ideals, then phi is an automorphism.
作者：
Du, Fan;Hua, Qiaoqiao;Wang, Chunhua;Wang, Qingfang
期刊：
Journal of Differential Equations,2024年393:102-138 ISSN：0022-0396
通讯作者：
Wang, CH
作者机构：
[Hua, Qiaoqiao; Wang, Chunhua; Du, Fan; Wang, CH] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Wang, Chunhua; Wang, CH] Cent China Normal Univ, Key Lab Nonlinear Anal & Applicat, Minist Educ, Wuhan 430079, Peoples R China.;[Wang, Qingfang] Wuhan Polytech Univ, Sch Math & Comp Sci, Wuhan 430023, Peoples R China.
通讯机构：
[Wang, CH ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Key Lab Nonlinear Anal & Applicat, Minist Educ, Wuhan 430079, Peoples R China.
摘要：
We revisit the following nonlinear critical elliptic equation -Delta u +V (vertical bar y'vertical bar,y '')u =u(N+2 /N-2), u > 0, u is an element of H-1(R-N), where (y', y '') is an element of R-3 x RN-3, V (vertical bar y vertical bar, y '') is a bounded non-negative function in R+ x RN-3. Assuming that r(2)V (r, y '')has a stable critical point (r(0), y(0)'') with r(0) > 0 and V (r(0), y(0)'') > 0, by using a modified finitedimensional reduction method and various local Pohozaev identities, we prove that the problem above has multi-piece of bubble solutions, whose energy can be made arbitrarily large. Since there involves a new variable (h) over bar in the concentrated points {x(j)(+/-)}(j=1)(m) during the reduction process, we have obtain a more precise estimate for the error term. And the bubble solutions are centered at points lying on the top and the bottom circles of a cylinder. Particularly, in one of these cases, the bubble solutions can concentrate at a pair of symmetric points relative to the origin. Our results present a new clustering type of blow-up phenomenon and we think the reason why this phenomenon can occur is mainly because that the function (r)2V (r, y '') has non-isolated critical points. (c) 2024 Elsevier Inc. All rights reserved.
摘要：
This paper deals with the following fractional Laplacian system with critical exponent: (−Δ)su=λ1u+μ1|u|2s∗−2u+β|u|2s∗2−2u|v|2s∗2,inΩ,(−Δ)sv=λ2v+μ2|v|2s∗−2v+β|v|2s∗2−2v|u|2s∗2,inΩ,u=v=0,inRN\Ω,$$ \left\{\begin{array}{ll}{\left(-\Delta \right)}&#x0005E;su&#x0003D;{\lambda}_1u&#x0002B;{\mu}_1{\left&#x0007C;u\right&#x0007C;}&#x0005E;{2_s&#x0005E;{\ast }-2}u&#x0002B;\beta {\left&#x0007C;u\right&#x0007C;}&#x0005E;{\frac{2_s&#x0005E;{\ast }}{2}-2}u{\left&#x0007C;v\right&#x0007C;}&#x0005E;{\frac{2_s&#x0005E;{\ast }}{2}},\kern0.30em & \mathrm{in}\kern3.0235pt \hspace{0.1em}\Omega, \\ {}{\left(-\Delta \right)}&#x0005E;sv&#x0003D;{\lambda}_2v&#x0002B;{\mu}_2{\left&#x0007C;v\right&#x0007C;}&#x0005E;{2_s&#x0005E;{\ast }-2}v&#x0002B;\beta {\left&#x0007C;v\right&#x0007C;}&#x0005E;{\frac{2_s&#x0005E;{\ast }}{2}-2}v{\left&#x0007C;u\right&#x0007C;}&#x0005E;{\frac{2_s&#x0005E;{\ast }}{2}},\kern0.30em & \mathrm{in}\kern3.0235pt \hspace{0.1em}\Omega, \\ {}u&#x0003D;v=0,& \mathrm{in}\kern3.0235pt \hspace{0.1em}{\mathfrak{R}}&#x0005E;N\backslash \Omega, \end{array}\right. $$ where Ω$$ \Omega $$ is a bounded smooth open connected set in RN,2s∗=2NN−2s$$ {\mathfrak{R}}&#x0005E;N,{2}_s&#x0005E;{\ast }&#x0003D;\frac{2N}{N-2s} $$ is the fractional critical Sobolev exponent, s∈(0,1),μ1,μ2>0,0<λ1,λ2<λ1(Ω)$$ s\in \left(0,1\right),{\mu}_1,{\mu}_2>0,0<{\lambda}_1,{\lambda}_2<{\lambda}_1\left(\Omega \right) $$ and λ1(Ω)$$ {\lambda}_1\left(\Omega \right) $$ is the first eigenvalue of fractional Laplacian (−Δ)s$$ {\left(-\Delta \right)}&#x0005E;s $$ under the condition u=0$$ u&#x0003D;0 $$ in RN\Ω$$ {\mathfrak{R}}&#x0005E;N\backslash \Omega $$. We prove that, for each fixed β∈−μ1μ2,0$$ \beta \in \left(-\sqrt{\mu_1{\mu}_2},0\right) $$ and λ1,λ2$$ {\lambda}_1,{\lambda}_2 $$ slightly smaller than λ1(Ω)$$ {\lambda}_1\left(\Omega \right) $$, the above system with N≥5s$$ N\ge 5s $$ admits a sign‐changing solution in the following sense: one component changes sign, while the other one is positive. Our result includes the lower dimensional case N∈[5s,6s)$$ N\in \left[5s,6s\right) $$. Compared with the classical Laplacian case, our problem is nonlocal and the first component of the solution is sign‐changing, some new difficulties arise and new arguments and estimates should be introduced.
作者机构：
[Liu, Ning; Cao, Yue] South China Univ Technol, Sch Math, Guangzhou 510640, Guangdong, Peoples R China.;[Jing, Naihuan] North Carolina State Univ, Dept Math, Raleigh, NC 27695 USA.;[Jing, Naihuan] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Jing, NH ] N;North Carolina State Univ, Dept Math, Raleigh, NC 27695 USA.;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
摘要：
As a spin analog of the plethystic Murnaghan-Nakayama rule for Schur functions, the plethystic Murnaghan-Nakayama rule for Schur Q-functions is established with the help of the vertex operator realization. This generalizes both the Murnaghan-Nakayama rule and the Pieri rule for Schur Q-functions. A plethystic Murnaghan-Nakayama rule for Hall-Littlewood functions is also investigated.
作者机构：
[Miao, Shujing; Li, Shuchao; Li, SC] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.;[Miao, Shujing; Li, Shuchao; Li, SC] Cent China Normal Univ, Key Lab NAA MOE, Wuhan 430079, Peoples R China.;[Wei, Wei] Shanghai Univ Engn Sci, Ctr Intelligent Comp & Appl Stat, Sch Math Phys & Stat, Shanghai 201620, Peoples R China.
通讯机构：
[Li, SC ] C;Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Key Lab NAA MOE, Wuhan 430079, Peoples R China.
摘要：
A graph G is said to be k -extendable if every matching of size k in G can be extended to a perfect matching of G, where k is a positive integer. We say G is 1 -excludable if for every edge e of G, there exists a perfect matching excluding e. In this paper, we first establish a lower bound on the size (resp. the spectral radius) of G to guarantee that G is k -extendable. Then we determine a lower bound on the size (resp. the spectral radius) of G to guarantee that G is 1 -excludable. All the corresponding extremal graphs are characterized. (c) 2024 Elsevier B.V. All rights reserved.
作者机构：
[Dong, Yueping; Zhang, Jun] School of Mathematics and Statistics, and Key Laboratory of Nonlinear Analysis & Applications (Ministry of Education), Central China Normal University, Wuhan, 430079, China;[Takeuchi, Yasuhiro] College of Science and Engineering, Aoyama Gakuin University, Kanagawa, 252-5258, Japan;[Peng, Zhihang] National Key Laboratory of Intelligent Tracking and Forecasting for Infectious Diseases, Chinese Center for Disease Control and Prevention, Beijing, 102206, China
通讯机构：
[Yueping Dong] S;[Zhihang Peng] N;National Key Laboratory of Intelligent Tracking and Forecasting for Infectious Diseases, Chinese Center for Disease Control and Prevention, Beijing, 102206, China<&wdkj&>School of Mathematics and Statistics, and Key Laboratory of Nonlinear Analysis & Applications (Ministry of Education), Central China Normal University, Wuhan, 430079, China
摘要：
Preventive treatment for people with latent Tuberculosis infection (LTBI) has aroused our great interest. In this paper, we propose and analyze a novel mathematical model of TB considering preventive treatment with media impact. The basic reproduction number R0 is defined by the next generation matrix method. In the case without media impact, we prove that the disease-free equilibrium is globally asymptotically stable (unstable) if R0<1(R0>1). Furthermore, we obtain that a unique endemic equilibrium exists when R0>1, which is globally asymptotically stable in the case of permanent immunity and no media impact. We fit the model to the newly reported TB cases data from 2009 to 2019 of four regions in China and estimate the parameters. And we estimated R0 =0.5013<1 in Hubei indicating that TB in Hubei will be eliminated in the future. However, the estimated R0 =1.015>1 in Henan, R0 =1.282>1 in Jiangxi and R0 =1.930>1 in Xinjiang imply that TB will continue to persist in these three regions without further prevention and control measures. Besides, sensitivity analysis is carried out to illustrate the role of model parameters for TB control. Our finding reveals that appropriately improving the rate of timely treatment for actively infected people and increasing the rate of individuals with LTBI seeking preventive treatment could achieve the goal of TB elimination. In addition, another interesting finding shows that media impact can only reduce the number of active infections to a limited extent, but cannot change the prevalence of TB.
期刊：
Journal of Differential Equations,2024年379:315-334 ISSN：0022-0396
通讯作者：
Wang, YC
作者机构：
[Wang, Yuchen; Wang, YC] Tianjin Normal Univ, Sch Math Sci, Tianjin 300387, Peoples R China.;[Wang, Yuchen] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Wang, YC ] T;Tianjin Normal Univ, Sch Math Sci, Tianjin 300387, Peoples R China.
关键词：
Rotating vortex patch;Kirchhoff ellipse patch;Concentrated vorticity;Conformal mapping;Robin function
摘要：
In this paper, we obtain families of uniformly rotating vorticity in the unit disk with a sufficiently large angular velocity. The solution is either a small nearly-ellipse vortex patch highly concentrated near the origin or a 2 + 1 vorticity configuration where another two vortical domains are sufficiently close to the boundary of fluid domain. The vorticity components are not necessarily symmetric nor small in the same order. These solutions are constructed via a perturbational approach and exhibit an interesting multi-scale phenomenon in the planar vortex flows. (c) 2023 Elsevier Inc. All rights reserved.
期刊：
Advances in Mathematics,2024年442:109569 ISSN：0001-8708
通讯作者：
Naihuan Jing
作者机构：
[Naihuan Jing] Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA;[Jian Zhang] School of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei 430079, China
通讯机构：
[Naihuan Jing] D;Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA
摘要：
We explore the invariant theory of quantum symmetric spaces of orthogonal and symplectic types by employing R-matrix techniques. Our focus involves establishing connections among the quantum determinant, Sklyanin determinants associated with the orthogonal and symplectic cases, and the quantum Pfaffians over the symplectic quantum space. Drawing inspiration from twisted Yangians, we not only demonstrate but also extend the applicability of q-Jacobi identities, q-Cayley's complementary identities, q-Sylvester identities, and Muir's theorem to Sklyanin minors in both orthogonal and symplectic types, along with q-Pfaffian analogs in the symplectic scenario. Furthermore, we present expressions for Sklyanin determinants and quantum Pfaffians in terms of quasideterminants.
作者机构：
[Chen, Haixia] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Pistoia, Angela] Sapienza Univ Roma, Dipartimento Sci Base & Applicate Ingn, Via Scarpa 16, I-00161 Rome, Italy.
通讯机构：
[Pistoia, A ] S;Sapienza Univ Roma, Dipartimento Sci Base & Applicate Ingn, Via Scarpa 16, I-00161 Rome, Italy.
关键词：
Schrodinger systems;segregated solutions;large number of components
摘要：
In this paper we are concerned with the existence of segregated non-radial solutions for nonlinear Schrodinger systems with a large number of components in a weak fully attractive or repulsive regime in presence of a suitable external radial potential.
期刊：
LINEAR & MULTILINEAR ALGEBRA,2024年 ISSN：0308-1087
通讯作者：
Wei, W
作者机构：
[Wei, Wei] Shanghai Univ Engn Sci, Ctr Intelligent Comp & Appl Stat, Sch Math Phys & Stat, Shanghai, Peoples R China.;[Feng, Zhimin] Cent China Normal Univ, Fac Math & Stat, Wuhan, Peoples R China.;[Feng, Zhimin] Xinyang Normal Univ, Sch Math & Stat, Xinyang, Peoples R China.;[Wei, Wei; Wei, W] Shanghai Univ Engn Sci, Ctr Intelligent Comp & Appl Stat, Sch Math Phys & Stat, Shanghai 201620, Peoples R China.
通讯机构：
[Wei, W ] S;Shanghai Univ Engn Sci, Ctr Intelligent Comp & Appl Stat, Sch Math Phys & Stat, Shanghai 201620, Peoples R China.
关键词：
A(alpha)-spectral radius;size;diameter;double leading eigenvectors
摘要：
The A(alpha)-matrix of a graph G is defined as the convex linear combination of the adjacency matrix A(G) and the diagonal matrix of degrees D(G), i.e. A(alpha)(G)=alpha D(G)+(1-alpha)A(G)=alpha D(G)+(1-alpha)A(G) with alpha is an element of[0,1]. The maximum modulus among all A(alpha)-eigenvalues is called the A(alpha)-spectral radius. In this paper, we order the connected graphs with size m and diameter (at least) d from the second to the (left perpendiculard/2right perpendicular+1)th regarding to the A(alpha)-spectral radius for alpha is an element of[1/2,1). As by-products, we identify the first left perpendiculard/2 right perpendicular largest trees of order n and diameter (at least) d in terms of their A(alpha)-spectral radii, and characterize the unique graph with at least one cycle having the largest A(alpha)-spectral radius among graphs of size m and diameter (at least) d. Consequently, the corresponding results for signless Laplacian matrix can be deduced as well.
摘要：
The sterile insect technique is one of the effective biological measures for mosquitoes control. In this paper, a model of competition between two mosquito species with sterile mosquitoes is presented. We first formulated a simple competitive model as our baseline model. Then, we formulated an interactive model with wild and sterile mosquitoes of one type of species, followed by the introduction of one type of sterile mosquitoes into the baseline competitive model. We have considered the case in which the amount of sterile mosquitoes released per unit time is constant. We have investigated the existence and stability of equilibria of the model and derived some release thresholds, based on which, we have investigated the impact of releasing sterile mosquitoes on the dynamics of competition between different species of mosquitoes.
期刊：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B,2024年29(1):479-512 ISSN：1531-3492
通讯作者：
Jiang, JF
作者机构：
[Li, Yaoqi] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Jiang, Jifa; Jiang, JF] Shanghai Normal Univ, Math & Sci Coll, Shanghai, Peoples R China.
通讯机构：
[Jiang, JF ] S;Shanghai Normal Univ, Math & Sci Coll, Shanghai, Peoples R China.
关键词：
3D Ricker competitive system;Fine focus;Hopf bifurcation;Multiplicity of limit cycles
摘要：
Jiang and Niu [12] and Gyllenberg et al. [4] showed that nontrivial periodic orbits for three dimensional Ricker competitive system only occur in Jiang-Niu's classes $ 26-31 $. This paper proves that classes $ 27-31 $ for three dimensional Ricker competitive system admit at least three limit cycles, classes $ 26-31 $ possessing at least two limit cycles are also provided.
摘要：
This paper is concerned with the minimizers of L-2-subcritical constraint variational problems with spatially decaying nonlinearities in a bounded domain Omega of R-N (N >= 1). We prove that the problem admits minimizers for any M > 0. Moreover, the limiting behavior of minimizers as M -> infinity is also analyzed rigorously.
作者机构：
[Xiang, Changlin] China Three Gorges Univ, Gorges Math Res Ctr 3, Yichang 443002, Peoples R China.;[Zheng, Gaofeng] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Zheng, GF ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
关键词：
fourth order elliptic equation;regularity theory;Morrey space;decay estimates;Riesz potential
摘要：
This paper is a continuation of recent work by Guo-Xiang-Zheng [10]. We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Riviere equation Delta 2u=Delta(V backward difference u)+div(w backward difference u)+( backward difference omega+F)& sdot; backward difference u+fin B4,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta<^>{2}u=\Delta(V\nabla u)+{\text{div}}(w\nabla u)+(\nabla\omega+F)\cdot\nabla u+f\qquad\text{in}B<^>{4},$$\end{document} under the smallest regularity assumptions of V, omega, omega, F, where f belongs to some Morrey spaces. This work was motivated by many geometrical problems such as the flow of biharmonic mappings. Our results deepens the Lp type regularity theory of [10], and generalizes the work of Du, Kang and Wang [4] on a second order problem to our fourth order problems.
作者：
Gong, Di;Yang, Harrison Hao;Wu, Di;Dai, Jinjun
期刊：
Education and Information Technologies,2023年28(2):1715-1733 ISSN：1360-2357
通讯作者：
Harrison Hao Yang
作者机构：
[Gong, Di; Yang, Harrison Hao; Wu, Di] Cent China Normal Univ, Fac Artificial Intelligence Educ, Wuhan, Peoples R China.;[Yang, Harrison Hao] SUNY Coll Oswego, Sch Educ, Oswego, NY 13126 USA.;[Dai, Jinjun] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.
通讯机构：
[Harrison Hao Yang] F;Faculty of Artificial Intelligence in Education, Central China Normal University, Wuhan, China<&wdkj&>School of Education, State University of New York at Oswego, Oswego, USA
