具有梯度吸收项的非局部反应扩散方程解的性质
Properties of Solutions to Nonlocal Reaction-Diffusion Equations with Gradient Absorption Terms
DOI: 10.12677/PM.2023.136170, PDF,   
作者: 杨来君：兰州交通大学数理学院，甘肃 兰州
关键词: 全局存在；爆破；下界；吸收项；Global Existence； Blow-Up； Lower Bound； Absorption Term
摘要: 针对在非局部边界条件下具有梯度吸收项的反应扩散方程解的性质的问题，通过构造适当的辅助函数，利用散度定理、Hölder不等式、Young不等式、Sobolev不等式和微分不等式技巧，得到解的全局存在性和爆破时间的下界的估计。
Abstract: For the properties of solutions of reaction-diffusion equations with gradient absorption terms under non-local boundary conditions, by using auxiliary function, divergence theorem, Hölder inequalities, Young inequalities, Sobolev inequalities and a differential inequality technique, the global existence of the solutions and lower bound for blow-up time are derived.
文章引用：杨来君. 具有梯度吸收项的非局部反应扩散方程解的性质[J]. 理论数学, 2023, 13(6): 1668-1676. https://doi.org/10.12677/PM.2023.136170

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