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)u...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.展开更多
文摘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.
