Zeitschrift für angewandte Mathematik und Physik最新文献

On a quasilinear two-species chemotaxis system with general kinetic functions and interspecific competition 关于具有一般动力学函数和种间竞争的准线性双物种趋化系统

Zeitschrift für angewandte Mathematik und Physik Pub Date : 2024-09-17 DOI: 10.1007/s00033-024-02325-5

Yifeng Huili

{"title":"On a quasilinear two-species chemotaxis system with general kinetic functions and interspecific competition","authors":"Yifeng Huili","doi":"10.1007/s00033-024-02325-5","DOIUrl":"https://doi.org/10.1007/s00033-024-02325-5","url":null,"abstract":"In this paper, we study the following two-species chemotaxis system with generalized volume-filling effect and general kinetic functions $$begin{aligned} left{ begin{aligned} &u_t=nabla cdot (D_{1}(u)nabla u)- nabla cdot ( chi _{1}(u)nabla w) + f_{1}(u)-mu _{1}a_{1}uv,&(x,t)in Omega times (0,infty ), &v_t=nabla cdot (D_{2}(v)nabla v)- nabla cdot ( chi _{2}(v)nabla w) + f_{2}(v)-mu _{2}a_{2}uv,&(x,t)in Omega times (0,infty ), &tau w_t=Delta w - w + g_{1}(u) + g_{2}(v),&(x,t)in Omega times (0,infty ), end{aligned} right. end{aligned}$$under homogeneous Neumann boundary conditions in a smoothly bounded domain (Omega subset {mathbb {R}}^{n}) ((nge 1)), where (a_{1}, a_{2}, mu _{1}, mu _{2}) are positive constants. When the functions (D_{i}, S_{i}, f_{i}, g_{i}) ((i=1,2)) belong to (C^{2}) fulfilling some suitable hypotheses, we study the global existence and boundedness of classical solutions for the above system and find that under the case of (tau =1) or (tau =0), either the higher-order nonlinear diffusion or strong logistic damping can prevent blow-up of classical solutions for the problem. In addition, when the functions are replaced to Lotka–Volterra competitive kinetic functional response term and linear signal generations, by constructing some appropriate Lyapunov functionals, we show that the solution convergences to the constant steady state in (L^{infty }(Omega )) in the case of (a_1, a_2 in (0,1)) or (a_1 ge 1>a_2 > 0) under some more concise conditions than [2], which improved the existing conditions to some extent.","PeriodicalId":501481,"journal":{"name":"Zeitschrift für angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142255912","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Fractional wave equation with irregular mass and dissipation 具有不规则质量和耗散的分数波方程

Zeitschrift für angewandte Mathematik und Physik Pub Date : 2024-09-17 DOI: 10.1007/s00033-024-02321-9

Michael Ruzhansky, Mohammed Elamine Sebih, Niyaz Tokmagambetov

引用次数: 0

Multiplicity and concentration behavior of solutions for magnetic Choquard equation with critical growth 具有临界增长的磁性乔夸德方程溶液的多重性和浓度行为

Zeitschrift für angewandte Mathematik und Physik Pub Date : 2024-09-13 DOI: 10.1007/s00033-024-02318-4

Houzhi Tang

{"title":"Multiplicity and concentration behavior of solutions for magnetic Choquard equation with critical growth","authors":"Houzhi Tang","doi":"10.1007/s00033-024-02318-4","DOIUrl":"https://doi.org/10.1007/s00033-024-02318-4","url":null,"abstract":"In this paper, we consider the following nonlinear Choquard equation with magnetic field $$begin{aligned} begin{aligned} left{ begin{array}{l} displaystyle bigg (frac{varepsilon }{i}nabla -A(x)bigg )^{2}u+V(x)u=varepsilon ^{mu -N}left( ,,int limits _{{mathbb {R}}^{N}}frac{|u(y)|^{2_{mu }^{*}}+F(|u(y)|^{2})}{|x-y|^{mu }}text {d}yright) left( |u|^{2_{mu }^{*}-2}u+frac{1}{2_{mu }^{*}}f(|u|^{2})uright) hspace{1.14mm}text{ in }hspace{1mm} {mathbb {R}}^{N}, displaystyle uin H^{1}({mathbb {R}}^{N},{mathbb {C}}) end{array} right. end{aligned} end{aligned}$$where (varepsilon >0) is a small parameter, (Nge 3), (0<mu <N), (2_{mu }^{*}=frac{2N-mu }{N-2}), (V(x):{mathbb {R}}^{N}rightarrow {mathbb {R}}^{N}) and (A(x):{mathbb {R}}^{N}rightarrow {mathbb {R}}^{N}) is a continuous potential, f is a continuous subcritical term, and F is the primitive function of f. Under a local assumption on the potential V, by the variational methods, the penalization techniques and the Ljusternik–Schnirelmann theory, we prove the multiplicity and concentration properties of nontrivial solutions of the above problem for (varepsilon >0) small enough.","PeriodicalId":501481,"journal":{"name":"Zeitschrift für angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142255909","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Boundedness and finite-time blow-up in a Keller–Segel chemotaxis-growth system with flux limitation 具有流量限制的凯勒-西格尔趋化-生长系统中的有界性和有限时间膨胀

Zeitschrift für angewandte Mathematik und Physik Pub Date : 2024-09-12 DOI: 10.1007/s00033-024-02320-w

Chunmei Chen, Pan Zheng

{"title":"Boundedness and finite-time blow-up in a Keller–Segel chemotaxis-growth system with flux limitation","authors":"Chunmei Chen, Pan Zheng","doi":"10.1007/s00033-024-02320-w","DOIUrl":"https://doi.org/10.1007/s00033-024-02320-w","url":null,"abstract":"This paper deals with a parabolic–elliptic Keller–Segel chemotaxis-growth system with flux limitation $$begin{aligned} left{ begin{aligned} u_t&=nabla cdot ((u+1)^{m-1}nabla u)- nabla cdot (uf(|nabla v|^{2})nabla v)+lambda u-mu u^k,&quad xin Omega ,t>0, 0&=Delta v-M(t)+u,&quad xin Omega ,t>0, end{aligned} right. end{aligned}$$under homogeneous Neumann boundary conditions, where (Omega subset {mathbb {R}}^N) is a smoothly bounded domain, (min {mathbb {R}}), (lambda>0, mu >0), (k>1), (M(t):=frac{1}{|Omega |} mathop {int }limits _{Omega } u(x, t) d x), (fleft( |nabla v|^2right) =(1+|nabla v|^2)^{-alpha }, alpha in {mathbb {R}}). In this framework, it is shown that when (Nge 2, m+k>2, k>1, kge m) and $$begin{aligned} alpha >frac{4N-(m+k)N-2}{4(N-1)}, end{aligned}$$then for all nonnegative initial data, the solution is global and bounded in time. Moreover, when (Omega subset {mathbb {R}}^N) ((Nge 5)) is a ball, if (1<m<min left{ frac{2N-4}{N},1-frac{1}{N}+frac{1}{N}sqrt{N^2-4N+1}right} ) and the parameters (alpha ) and k satisfy suitable conditions, there exist some initial data (u_{0}) such that the solution u(x, t) blows up at finite time (T_{max }) in (L^{infty })-norm sense.","PeriodicalId":501481,"journal":{"name":"Zeitschrift für angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142189755","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Eventual smoothness in a chemotaxis-Navier–Stokes system with indirect signal production involving Dirichlet signal boundary condition 涉及迪里夏特信号边界条件的间接信号产生的趋化-纳维尔-斯托克斯系统中的最终平稳性

Zeitschrift für angewandte Mathematik und Physik Pub Date : 2024-09-12 DOI: 10.1007/s00033-024-02324-6

Chao Liu, Bin Liu

引用次数: 0

Global existence and exponential decay of strong solutions to the 3D nonhomogeneous nematic liquid crystal flows with density-dependent viscosity 具有密度相关粘度的三维非均相向列液晶流的强解的全局存在性和指数衰减

Zeitschrift für angewandte Mathematik und Physik Pub Date : 2024-09-12 DOI: 10.1007/s00033-024-02322-8

Huanyuan Li, Jieqiong Liu

引用次数: 0

Blow-up prevention by indirect signal production mechanism in a two-dimensional Keller–Segel–(Navier–)Stokes system 二维 Keller-Segel-(Navier-)Stokes 系统中通过间接信号产生机制防止炸裂

Zeitschrift für angewandte Mathematik und Physik Pub Date : 2024-09-10 DOI: 10.1007/s00033-024-02323-7

Jiashan Zheng, Xiuran Liu

{"title":"Blow-up prevention by indirect signal production mechanism in a two-dimensional Keller–Segel–(Navier–)Stokes system","authors":"Jiashan Zheng, Xiuran Liu","doi":"10.1007/s00033-024-02323-7","DOIUrl":"https://doi.org/10.1007/s00033-024-02323-7","url":null,"abstract":"This paper deals with an initial-boundary value problem in two-dimensional smoothly bounded domains for the system $$begin{aligned} left{ begin{array}{l} n_t+textbf{u}cdot nabla n=Delta n-nabla cdot (nmathcal {S}(n)nabla v),quad xin Omega , t>0, v_t+textbf{u}cdot nabla v=Delta v-v+w,quad xin Omega , t>0, w_t+textbf{u}cdot nabla w=Delta w-w+n,quad xin Omega , t>0, textbf{u}_t+kappa (textbf{u}cdot nabla )textbf{u}+nabla P=Delta textbf{u}+nnabla phi , quad xin Omega , t>0, nabla cdot textbf{u}=0,quad xin Omega , t>0, end{array}right. qquad qquad (*) end{aligned}$$which describes the mutual interaction of chemotactically moving microorganisms and their surrounding incompressible fluid, where (kappa in mathbb {R}), the gravitational potential (phi in W^{2,infty }(Omega )), and (mathcal {S}(n)) satisfies $$begin{aligned} |mathcal {S}(n)|le C_mathcal {S}(1+n)^{-alpha } quad text{ for } text{ all }~~ nge 0,~~C_mathcal {S}>0~~text{ and }~~alpha >-1. end{aligned}$$Under the boundary conditions $$begin{aligned} (nabla n-nmathcal {S}(n)nabla v)cdot nu =partial _nu v=partial _nu w=0, textbf{u}=0, quad xin partial Omega , t>0, end{aligned}$$it is shown in this paper that suitable regularity assumptions on the initial data entail the following: (i) If (alpha >-1) and (kappa =0), then the simplified chemotaxis-Stokes system possesses a unique global classical solution which is bounded. (ii) If (alpha ge 0) and (kappa in mathbb {R}), then the full chemotaxis-Navier–Stokes system admits a unique global classical solution.\u0000","PeriodicalId":501481,"journal":{"name":"Zeitschrift für angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142189697","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Wave mode conversion in isotropic halfspace 各向同性半空间中的波模转换

Zeitschrift für angewandte Mathematik und Physik Pub Date : 2024-09-07 DOI: 10.1007/s00033-024-02319-3

Sergey V. Kuznetsov

引用次数: 0

Investigating analytical and numerical techniques for the $$(2+1) {mathfrak {q}}$$ -deformed equation 研究 $$(2+1) {mathfrak {q}}$ 变形方程的分析和数值技术

Zeitschrift für angewandte Mathematik und Physik Pub Date : 2024-09-06 DOI: 10.1007/s00033-024-02313-9

Khalid K. Ali, Mohamed S. Mohamed, Weam G. Alharbi

{"title":"Investigating analytical and numerical techniques for the $$(2+1) {mathfrak {q}}$$ -deformed equation","authors":"Khalid K. Ali, Mohamed S. Mohamed, Weam G. Alharbi","doi":"10.1007/s00033-024-02313-9","DOIUrl":"https://doi.org/10.1007/s00033-024-02313-9","url":null,"abstract":"This paper presents a comprehensive study of a model called the ((2+1) {mathfrak {q}})-deformed tanh-Gordon model. This model is particularly useful for studying physical systems with violated symmetries, as it provides insights into their behavior. To solve the ((2+1) {mathfrak {q}})-deformed equation for specific parameter values, the (({mathfrak {H}}+frac{{mathcal {G}}^{prime }}{ {mathcal {G}}^{2}}))-expansion approach is employed. This technique generates analytical solutions that reveal valuable information about the system’s dynamics and behavior. These solutions offer insights into the underlying mathematics and deepen the understanding of the system’s properties. To validate the accuracy of the analytical solutions, the finite difference technique is also used to find a numerical solution to the ({mathfrak {q}})-deformed equation. This numerical approach ensures the correctness of the solutions and enhances the reliability of the results. Tables and graphics are presented in the publication to aid comprehension and comparison. These visuals improve the clarity and interpretability of the data, allowing readers to better understand the similarities and differences between the analytical and numerical solutions.","PeriodicalId":501481,"journal":{"name":"Zeitschrift für angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142224638","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Global boundedness and large time behavior of solutions to a chemotaxis-convection model of capillary-sprout growth during tumor angiogenesis 肿瘤血管生成过程中毛细血管喷出生长的趋化-对流模型解的全局有界性和大时间行为

Zeitschrift für angewandte Mathematik und Physik Pub Date : 2024-09-02 DOI: 10.1007/s00033-024-02317-5

Chun Wu

引用次数: 0