具有逻辑源的吸引-排斥模型的全局可解性和有界性

IF 1.7 4区 数学 Q1 Mathematics
Danqing Zhang
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引用次数: 0

摘要

在本文中,我们将讨论一个具有逻辑源的吸引-排斥模型,具体如下:$$\begin{aligned}\contextstyle\begin{cases}{u_{t}} = \Delta u - \chi \nabla \cdot (u \nabla v) + \xi \nabla \cdot (u \nabla w) + \mu {u^{q}}(1 - u) &\text{in }Q , \ {v_{t}} = \Delta v - {\alpha _{1}}v + {\beta _{1}}u &\text{in }Q , \ {w_{t}} = \Delta w - {\alpha _{2}}w + {\beta _{2}}u & (text{in }Q , \end{cases}\displaystyle \end{aligned}$$ 其中 $Q = \Omega \times {mathbb{R}^{+} }$ , $Omega \subset {mathbb{R}^{3}}$ 是一个有界域。我们主要关注逻辑阻尼对该模型全局可解性的影响。在维度 2 中,q 可以等于 1(Math.方法应用科学》39(2):289-301, 2016)。在维度 3 中,我们推导出当 $q>\frac{8}{7}$ 时,该问题存在全局有界解。 事实上,我们通过迭代法将估计难度转移到了逻辑项上,因此,与《数学分析》(J. Math. Anal.Anal.Appl. 2:448 2017; Z. Angew.Math.Phys. 73(2):1-25 2022)在维 3 中的结果相比,我们的结果不需要对系数进行任何限制。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Global solvability and boundedness to a attraction–repulsion model with logistic source
In this paper, we deal with an attraction–repulsion model with a logistic source as follows: $$\begin{aligned} \textstyle\begin{cases} {u_{t}} = \Delta u - \chi \nabla \cdot (u \nabla v) + \xi \nabla \cdot (u \nabla w) + \mu {u^{q}}(1 - u) &\text{in } Q , \\ {v_{t}} = \Delta v - {\alpha _{1}}v + {\beta _{1}}u &\text{in } Q , \\ {w_{t}} = \Delta w - {\alpha _{2}}w + {\beta _{2}}u & \text{in } Q , \end{cases}\displaystyle \end{aligned}$$ where $Q = \Omega \times {\mathbb{R}^{+} }$ , $\Omega \subset {\mathbb{R}^{3}}$ is a bounded domain. We mainly focus on the influence of logistic damping on the global solvability of this model. In dimension 2, q can be equal to 1 (Math. Methods Appl. Sci. 39(2):289–301, 2016). In dimension 3, we derive that the problem admits a global bounded solution when $q>\frac{8}{7}$ . In fact, we transfer the difficulty of estimation to the logistic term through iterative methods, thus, compared to the results in (J. Math. Anal. Appl. 2:448 2017; Z. Angew. Math. Phys. 73(2):1–25 2022) in dimension 3, our results do not require any restrictions on the coefficients.
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来源期刊
Boundary Value Problems
Boundary Value Problems MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
3.00
自引率
5.90%
发文量
83
审稿时长
4 months
期刊介绍: The main aim of Boundary Value Problems is to provide a forum to promote, encourage, and bring together various disciplines which use the theory, methods, and applications of boundary value problems. Boundary Value Problems will publish very high quality research articles on boundary value problems for ordinary, functional, difference, elliptic, parabolic, and hyperbolic differential equations. Articles on singular, free, and ill-posed boundary value problems, and other areas of abstract and concrete analysis are welcome. In addition to regular research articles, Boundary Value Problems will publish review articles.
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