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 $u_t = ∆u+k∆u_t+w(x)u^p (x,t).$ In [1], Li et al. gave the critical Fujita exponent, second critical exponent and the life span for blow-up solutions under $w(x) = |x|^σ$ with $σ >0.$ We further generalize the weight function $w(x) ∼ |x|^σ$ for $−2<σ<0,$ and discuss the global and non-global solutions to obtain the critical Fujita exponent.