全抛物线营养税系统解的全局可解性和渐近行为

IF 1.2 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Journal of Mathematical Physics Pub Date : 2024-08-21 DOI:10.1063/5.0212819

Hanqi Huang, Guoqiang Ren, Xing Zhou

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引用次数: 0

摘要

在本文中，我们考虑了全抛物线 nu'trient taxis 系统：ut = d1Δu -∇ - (ϕ(u, v)∇v), vt = d2Δv - ξug(v) - μv + r(x, t), x∈ Ω, t > 0，该系统在具有光滑边界的凸有界域中的同质 Neumann 边界条件下。我们证明，该系统在任意维度的域中都有一个全局有界经典解，在高维域中至少有一个全局广义解。此外，我们还讨论了广义解的渐近行为。我们的结果不仅概括并部分改进了之前已知的发现，还引入了新的见解。

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Global solvability and asymptotic behavior of solutions for a fully parabolic nutrient taxis system

In this paper, we consider the fully parabolic nu’trient taxis system: ut = d1Δu − ∇ · (ϕ(u, v)∇v), vt = d2Δv − ξug(v) − μv + r(x, t), x ∈ Ω, t > 0 under homogeneous Neumann boundary conditions in a convex bounded domain with smooth boundary. We show that the system possesses a global bounded classical solution in domains of arbitrary dimension and at least one global generalized solution in high-dimensional domain. In addition, the asymptotic behavior of generalized solutions is discussed. Our results not only generalize and partly improve upon previously known findings but also introduce new insights.

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来源期刊

Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

2.20

自引率

15.40%

发文量

396

审稿时长

4.3 months

期刊介绍： Since 1960, the Journal of Mathematical Physics (JMP) has published some of the best papers from outstanding mathematicians and physicists. JMP was the first journal in the field of mathematical physics and publishes research that connects the application of mathematics to problems in physics, as well as illustrates the development of mathematical methods for such applications and for the formulation of physical theories. The Journal of Mathematical Physics (JMP) features content in all areas of mathematical physics. Specifically, the articles focus on areas of research that illustrate the application of mathematics to problems in physics, the development of mathematical methods for such applications, and for the formulation of physical theories. The mathematics featured in the articles are written so that theoretical physicists can understand them. JMP also publishes review articles on mathematical subjects relevant to physics as well as special issues that combine manuscripts on a topic of current interest to the mathematical physics community. JMP welcomes original research of the highest quality in all active areas of mathematical physics, including the following: Partial Differential Equations Representation Theory and Algebraic Methods Many Body and Condensed Matter Physics Quantum Mechanics - General and Nonrelativistic Quantum Information and Computation Relativistic Quantum Mechanics, Quantum Field Theory, Quantum Gravity, and String Theory General Relativity and Gravitation Dynamical Systems Classical Mechanics and Classical Fields Fluids Statistical Physics Methods of Mathematical Physics.