@Article{JPDE-37-263,
author = {Li , Fang and Zhang , Jingjing},
title = {Blow-Up of Solution and Energy Decay for a Quasilinear Parabolic Problem},
journal = {Journal of Partial Differential Equations},
year = {2024},
volume = {37},
number = {3},
pages = {263--277},
abstract = {<div style="text-align: justify;">In this paper, we obtain the blow-up result of solutions and some general decay rates for a quasilinear parabolic equation with viscoelastic terms $$A(t)|u_{t}|^{m-2}u_{t}-\Delta u+\int_0^{t}g(t-s)\Delta u(x,s){\rm d}s=|u|^{p-2}u\log |u|.$$ 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 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 $g&#39;\leq -\xi(t)H(g(t)),~H(t)=t^\nu,~t\geq 0,~\nu&gt;1$. This improves the existing results.</div>},
issn = {2079-732X},
doi = {https://doi.org/10.4208/jpde.v37.n3.3},
url = {http://global-sci.org/intro/article_detail/jpde/23342.html}
}