首页|Blow-Up of Solution and Energy Decay for a Quasilinear Parabolic Problem
Blow-Up of Solution and Energy Decay for a Quasilinear Parabolic Problem
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In this paper,we obtain the blow-up result of solutions and some general decay rates for a quasilinear parabolic equation with viscoelastic terms A(t)|ut|m-2ut-△u+∫t0g(t-s)△u(x,s)ds=|u|p-2ulog|u|.Due to the presence of the log source term,it is not possible to use the source term to dominate the term A(t)|ut|m-2ut.To bypass this difficulty,we build up inverse Hölder-like inequality and then apply differential inequality argument to prove the solution blows up in finite time.In addition,we can also give a decay rate under a general assumption on the relaxation functions satisfying g'≤-ξ(t)H(g(t)),H(t)=tv,t ≥ 0,v＞1.This improves the existing results.
Viscoelastic termblow updecay estimate
LI Fang、ZHANG Jingjing
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School of Mathematics,Jilin University,Changchun 130012,China
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