Year: 2019
Author: Yuhua Jian, Zuodong Yang
Journal of Mathematical Study, Vol. 52 (2019), Iss. 2 : pp. 111–126
Abstract
This paper is devoted to a $p(x)$-Laplace equation with Dirichlet boundary. We obtain the existence of global solution to the problem by employing the method of potential wells. On the other hand, we show that the solution will blow up in finite time with $u_0 \not\equiv 0$ and nonpositive initial energy functional $J(u_0).$ By defining a positive function $F(t)$ and using the method of concavity we find an upper bound for the blow-up time.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v52n2.19.01
Journal of Mathematical Study, Vol. 52 (2019), Iss. 2 : pp. 111–126
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: $p(x)$-Laplace equation global weak solution finite time blow-up upper bounds.