Blow-Up of Solution and Energy Decay for a Quasilinear Parabolic Problem  

作　　者：LI Fang ZHANG Jingjing 

机构地区：[1]School of Mathematics,Jilin University,Changchun 130012,China

出　　处：《Journal of Partial Differential Equations》2024年第3期263-277,共15页偏微分方程（英文版）

摘　　要：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)|u_(t)|^(m-2)u_(t)-△u+∫_(0)^(t)g(t-s)△u(t-s)△(x,s)ds=|u|^(p-2)ulog|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)|u_(t)|^(m-2)u_(t).To bypass this difficulty,we build up inverse Holder-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′≤-ζ(t)H(g(t),H(t))=t^(v),t≥0,v>1.This improves the existing results.

关 键 词：Viscoelastic term blow up decay estimate 

分 类 号：O145.8[理学—数学]