Some interesting special cases of a non-local problem modelling ohmic heating with variable thermal conductivity

被引：8

作者：

Tzanetis, DE ^{[1
]}

Vlamos, PM ^{[1
]}

机构：

[1] Natl Tech Univ Athens, Fac Sci Appl, Dept Math, Athens 15780, Greece

来源：

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY | 2001年 / 44卷

关键词：

non-local parabolic equations; blow-up; stability; local and global existence; stationary solutions;

D O I：

10.1017/S0013091500000109

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The non-local equation u(t) = (u(3)u(x))x + lambdaf(u)/(integral (1/)(-1)f(u)dx)(2) is considered, subject to some initial and Dirichlet boundary conditions. Here f is taken to be either exp(-s(4)) or H(1 - s) with H the Heaviside function, which are both decreasing. It is found that there exists a critical value lambda* = 2, so that for lambda > lambda* there is no stationary solution and u 'blows up' (in some sense). If 0 < lambda < lambda*, there is a unique stationary solution which is asymptotically stable and the solution of the IBVP is global in time.

引用

页码：585 / 595

页数：11

共 44 条

[1] A nonlocal problem modelling ohmic heating with variable thermal conductivity
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[2] Behaviour of a non-local reactive convective problem modelling Ohmic heating of foods
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