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Complete blow-up for degenerate semilinear parabolic equations

Authors
Journal
Journal of Computational and Applied Mathematics
0377-0427
Publisher
Elsevier
Publication Date
Volume
113
Identifiers
DOI: 10.1016/s0377-0427(99)00266-6
Keywords
  • Complete Blow-Up
  • Degenerate Semilinear Parabolic Equations

Abstract

Abstract Let T⩽∞,a,q and x0 be constants with a>0,q⩾0 and 0<x0<a. Existence of a unique solution u is established for the following degenerate semilinear parabolic initial-boundary value problem:xqut−uxx=f(u(x0,t)),0<x<a,0<t<T,u(x,0)=u0(x)⩾0,0⩽x⩽a,u(0,t)=u(a,t)=0,0<t<T,where f and u0 are given functions. We show that under certain conditions, u blows up in a finite time, and the set of blow-up points is the entire interval [0,a].

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