Blow-up problem for semilinear heat equation with nonlinear nonlocal boundary condition

被引：23

作者：

Gladkov, Alexander ^{[1
]}

Kavitova, Tatiana ^{[2
]}

机构：

[1] Belarusian State Univ, Dept Mech & Math, Nezavisimosti Ave 4, Minsk 220030, BELARUS

[2] Vitebsk State Univ, Dept Math, Moskovskii Pr 33, Vitebsk 210038, BELARUS

来源：

APPLICABLE ANALYSIS | 2016年 / 95卷 / 09期

关键词：

semilinear heat equation; nonlocal boundary condition; blow-up; POROUS-MEDIUM EQUATION; ASYMPTOTIC-BEHAVIOR; GLOBAL EXISTENCE; WEIGHT-FUNCTIONS; SYSTEM; ROLES;

D O I：

10.1080/00036811.2015.1080353

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider a semilinear parabolic equation with nonlinear nonlocal boundary condition and nonnegative initial datum. We prove some global existence results. Criteria on this problem which determine whether the solutions blow up in finite time for large or for all nontrivial initial data are also given. Moreover, we show that under certain conditions blow-up occurs only on the boundary.

引用

页码：1974 / 1988

页数：15

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