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

Xu Runzhang

Mathematics and Computers in Simulation (MATCOM), 2009, vol. 80, issue 4, 808-813

Abstract: 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.

Keywords: Semilinear parabolic equations; Initial boundary value; Potential wells; Asymptotic behavior; Blow up (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:80:y:2009:i:4:p:808-813

DOI: 10.1016/j.matcom.2009.08.028

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