Blow-up time and blow-up rate for pseudo-parabolic equations with weighted source
Commun. Korean Math. Soc.
Published online September 7, 2020
Huafei Di and Yadong Shang
Guangzhou University
Abstract : In this paper, we are concerned with the blow-up phenomena for a class of pseudo-parabolic equations with weighted source $u_{t}-\triangle u-\triangle u_{t}=a(x)f(u)$ subject to Dirichlet (or Neumann) boundary conditions in any smooth bounded domain $\Omega\subset \mathbb{R}^{n}$ $(n\geq1)$. Firstly, we obtain the upper and lower bounds for blow-up time of solutions to these problems. Moreover, we also give the estimates of blow-up rate of solutions under some suitable conditions. Finally, three models are presented to illustrate our main results. In some special cases, we can even get some exact values of blow-up time and blow-up rate.
Keywords : Pseudo-parabolic equation, Upper and lower bounds, Blow-up rate, Weighted source
MSC numbers : 35K70; 35K61; 35B44; 35D40
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