Blow-up phenomena of solutions for a reaction-diffusion equation with weighted exponential nonlinearity

Ma Lingwei; Fang Zhong Bo

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Blow-up phenomena of solutions for a reaction-diffusion equation with weighted exponential nonlinearity

机译：具有加权指数非线性的反应扩散方程解的爆破现象

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摘要

Blow-up phenomena for a reaction-diffusion equation with weighted exponential reaction term and null Dirichlet boundary condition are investigated. We establish sufficient conditions to guarantee existence of global solution or blow-up solution under appropriate measure sense by virtue of the method of super-sub solutions, the Bernoulli equation and the modified differential inequality techniques. Moreover, upper and lower bounds for the blow-up time are found in higher dimensional spaces and some examples for application are presented. (C) 2018 Elsevier Ltd. All rights reserved.

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《Computers & mathematics with applications》 |2018年第8期|2735-2745|共11页
作者
Ma Lingwei; Fang Zhong Bo;
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作者单位

Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China;

Ocean Univ China, Sch Math Sci, Qingdao 266100, Peoples R China;

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正文语种 eng
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关键词
Reaction-diffusion equation; Weight function; Exponential reaction; Bounds for blow-up time;

机译：反应扩散方程权函数指数反应爆炸时间界;

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1. Time-weighted blow-up rates and pointwise profile for single-point blow-up solutions in reaction-diffusion equations [J] . Liu Bingchen, Li Fengjie Mathematical Methods in the Applied Sciences . 2017,第14期

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2. Blow-up phenomena for a class of nonlinear reaction-diffusion equations under nonlinear boundary conditions [J] . Zhang Ling-Ling, Tian Hui-Min Applicable Analysis . 2019,第13a16期

机译：非线性边界条件下一类非线性反应扩散方程的爆破现象
3. Blow-Up Phenomena for Nonlinear Reaction-Diffusion Equations under Nonlinear Boundary Conditions [J] . Juntang Ding Journal of Function Spaces . 2016,第1期

机译：非线性边界条件下非线性反应扩散方程的爆破现象
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. Global existence of solutions to nonlinear wave equations by weighted Strichartz inequalities. [D] . Alpay, Nimet. 2004

机译：加权Strichartz不等式对非线性波动方程解的整体存在性。
6. Blow-up of solutions of nonlinear wave equations in three space dimensions [O] . Fritz John 1979

机译：三维空间中非线性波动方程解的爆破
7. Blow-up set for a semilinear heat equation with exponential nonlinearity (Analysis on non-equilibria and nonlinear phenomena : from the evolution equations point of view) [O] . Fujishima Yohei 2012

机译：具有指数非线性的半线性热方程的爆破集（非平衡和非线性现象的分析：从演化方程的角度来看）

Blow-up phenomena of solutions for a reaction-diffusion equation with weighted exponential nonlinearity

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