๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Blow-up for a nonlocal parabolic equation

โœ Scribed by Fei Liang; Yuxiang Li

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
643 KB
Volume
71
Category
Article
ISSN
0362-546X

No coin nor oath required. For personal study only.

โœฆ Synopsis

In this paper, we consider the blow-up properties of the radial solutions of the nonlocal parabolic equation

with homogeneous Dirichlet boundary condition, where ฮป, p > 0, 0 < ฮฑ โ‰ค 1. The criteria for the solutions to blow-up in finite time is given. It is proved that the blow-up is global and uniform for 0 < ฮฑ < 1, global and nonuniform for ฮฑ = 1. The blow-up rate of |u| โˆž is also determined.

๐Ÿ“œ SIMILAR VOLUMES

Blow-up for a degenerate parabolic equat
Blow-up for a degenerate parabolic equation with a nonlocal source
โœ Qilin Liu; Youpeng Chen; Chunhong Xie ๐Ÿ“‚ Article ๐Ÿ“… 2003 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 156 KB

In this paper, we investigate the blowup properties of the positive solutions to the following nonlocal degenerate parabolic equation with homogeneous Dirichlet boundary conditions in the interval (0, l), where 0 < ฮฑ < 2, p 1 q 1 > m > 1. We first establish the local existence and uniqueness of its

Properties of non-simultaneous blow-up s
Properties of non-simultaneous blow-up solutions in nonlocal parabolic equations
โœ Bingchen Liu; Fengjie Li ๐Ÿ“‚ Article ๐Ÿ“… 2010 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 596 KB

This paper deals with blow-up solutions in parabolic equations coupled via nonlocal nonlinearities, subject to homogeneous Dirichlet conditions. Firstly, some criteria on nonsimultaneous and simultaneous blow-up are given, including four kinds of phenomena: (i) the existence of non-simultaneous blow