Blow-up analyses in reaction-diffusion equations with nonlinear nonlocal boundary flux

Liu Bingchen; Lin Hongyan; Li Fengjie; Wang Xiangyu

首页> 外文期刊>ZAMP: Zeitschrift fur Angewandte Mathematik und Physik: = Journal of Applied Mathematics and Physics: = Journal de Mathematiques et de Physique Appliquees >Blow-up analyses in reaction-diffusion equations with nonlinear nonlocal boundary flux

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Blow-up analyses in reaction-diffusion equations with nonlinear nonlocal boundary flux

机译：非线性非局部边界通量反应扩散方程中的爆破分析

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摘要

In this paper, we study a reaction-diffusion system involving coupled sources and nonlinear nonlocal boundary flux. By using the comparison principle, we give the criteria on blow-up and global solutions. There exist no nontrivial global solutions under some conditions on the coefficients. After classifying simultaneous and non-simultaneous blow-up of the components of solutions, we obtain blow-up rates and sets. Lower and upper bounds of blow-up time are determined quantificationally for all dimensions of the space domains.

机译：在本文中，我们研究了涉及耦合源和非线性非本体边界通量的反应扩散系统。通过使用比较原理，我们提供爆炸和全球解决方案的标准。在系数上的某些条件下没有非活动全局解决方案。在分类解决方案组件的同时和非同时爆炸之后，我们获得了爆破速率和套件。用于空间域的所有尺寸确定吹气时间的下限和上限。

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来源
《ZAMP: Zeitschrift fur Angewandte Mathematik und Physik: = Journal of Applied Mathematics and Physics: = Journal de Mathematiques et de Physique Appliquees》 |2019年第4期|共27页
作者
Liu Bingchen; Lin Hongyan; Li Fengjie; Wang Xiangyu;
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作者单位

China Univ Petr Coll Sci Qingdao 266580 Shandong Peoples R China;

China Univ Petr Coll Sci Qingdao 266580 Shandong Peoples R China;

China Univ Petr Coll Sci Qingdao 266580 Shandong Peoples R China;

China Univ Petr Coll Sci Qingdao 266580 Shandong Peoples R China;

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原文格式 PDF
正文语种 eng
中图分类应用数学;
关键词
Reaction-diffusion equations; Nonlinear nonlocal boundary flux; Non-simultaneous blow-up; Blow-up rate; Blow-up time;

机译：反应扩散方程;非线性非本体边界通量;非同时爆炸;爆破率;爆炸时间;

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专利

1. Blow-up analyses in reaction-diffusion equations with nonlinear nonlocal boundary flux [J] . Liu Bingchen, Lin Hongyan, Li Fengjie, ZAMP: Zeitschrift fur Angewandte Mathematik und Physik: = Journal of Applied Mathematics and Physics: = Journal de Mathematiques et de Physique Appliquees . 2019,第4期

机译：非线性非局部边界通量反应扩散方程中的爆破分析
2. Asymptotic properties of blow-up solutions in reaction-diffusion equations with nonlocal boundary flux [J] . Liu Bingchen, Dong Mengzhen, Li Fengjie ZAMP: Zeitschrift fur Angewandte Mathematik und Physik: = Journal of Applied Mathematics and Physics: = Journal de Mathematiques et de Physique Appliquees . 2018,第2期

机译：非识别边界通量反应扩散方程中吹血溶液的渐近性能
3. Blow-up estimate in a reaction-diffusion equation with nonlinear nonlocal flux and source [J] . Liu Bingchen, Wu Guicheng, Sun Xizheng, Computers & mathematics with applications . 2019,第6期

机译：具有非线性非局部通量和源的反应扩散方程的爆破估计
4. Global existence and blow-up solutions for a class of nonlinear reaction diffusion equations under nonlinear boundary flux [C] . Yang Yan, Zhang Lingling Chinese Control and Decision Conference . 2019

机译：非线性边界通量下一类非线性反应扩散方程的整体存在和爆破解
5. Blow-Up Problems for the Heat Equation with Local Nonlinear Neumann Boundary Conditions [D] . Yang, Xin. 2017

机译：局部非线性Neumann边界条件的热方程的爆破问题
6. Rogue waves in the two dimensional nonlocal nonlinear Schrödinger equation and nonlocal Klein-Gordon equation [O] . Wei Liu, Jing Zhang, Xiliang Li 2012

机译：二维非局部非线性Schrödinger方程和非局部Klein-Gordon方程中的无赖波
7. Localization on the boundary of blow-up for reaction-diffusion equations with nonlinear boundary conditions. [O] . Arrieta Algarra José María, Rodríguez Bernal Aníbal 2020

机译：具有非线性边界条件的反应扩散方程爆破边界的局部化。
8. Equivalence of the Ewald-Oseen Extinction Theorem as a Nonlocal Boundary-Value Problem with Maxwell's Equations and Boundary Conditions. [R] . Dialetis, D. 1977

机译：作为具有麦克斯韦方程和边界条件的非局部边值问题的Ewald-Oseen灭绝定理的等价性。

Blow-up analyses in reaction-diffusion equations with nonlinear nonlocal boundary flux

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