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

This paper considers the Cauchy problem of pseudo-parabolic equation with inhomogeneous terms u(t)= triangle u+k triangle 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 sigma >0. We further generalize the weight function w(x) similar to| x| (sigma )for -2< sigma <0, and discuss the global and non-global solutions to obtain the critical Fujita exponent.