Asymptotic behavior and blow up of solutions for semilinear parabolic equations at critical energy level

In this paper we study the initial boundary value problem of semilinear parabolic equations with semilinear term f(u). By using the family of potential wells method we prove that if f(u) satisfies some conditions, J(u0)≤d and I(u0)>0, then the solution decays to zero exponentially as t→∞. On the other hand, if J(u0)≤d, I(u0)<0, then the solution blows up in finite time.

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Year of publication:	2009
Authors:	Runzhang, Xu
Published in:	Mathematics and Computers in Simulation (MATCOM). - Elsevier, ISSN 0378-4754. - Vol. 80.2009, 4, p. 808-813
Publisher:	Elsevier
Subject:	Semilinear parabolic equations \| Initial boundary value \| Potential wells \| Asymptotic behavior \| Blow up

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10011050498