Global and Nonglobal Solutions for Pseudo-Parabolic Equation with Inhomogeneous Terms

Abstract

This paper considers the Cauchy problem of pseudo-parabolic equation with inhomogeneous terms $u_{t}=\Delta u+k \Delta u_{t}+w(x) u^{p}(x, t).$ In [1], Li et al. gave the critical Fujita exponent, second critical exponent and the life span for blow-up solutions under $w(x)=|x|^{\sigma}$ with σ>0. We further generalize the weight function $w(x) \sim|x|^{\sigma}$ for −2<σ<0, and discuss the global and non-global solutions to obtain the critical Fujita exponent.

Keywords

Pseudo-parabolic equation / critical Fujita exponent / global solutions / blow-up