BLOW-UP TIME AND BLOW-UP RATE FOR PSEUDO-PARABOLIC EQUATIONS WITH WEIGHTED SOURCE

Abstract

In this paper, we are concerned with the blow-up phenomena for a class of pseudo-parabolic equations with weighted source ut−4u− 4ut = a(x)f(u) subject to Dirichlet (or Neumann) boundary conditions in any smooth bounded domain Ω ⊂ Rn (n ≥ 1). 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.