Title : ( Existence and blow up of solutions to a Petrovsky equation with memory and nonlinear source term )
Authors: Faramarz Tahamtani , Mohammad Shahrouzi ,
Full TextAbstract
We consider the semilinear Petrovsky equation utt + Δ2u − t0 g(t − s)Δ2u(s)ds = |u|pu in a bounded domain and prove the existence of weak solutions. Furthermore, we show that there are solutions under some conditions on initial data which blow up in finite time with non-positive initial energy as well as positive initial energy. Estimates of the lifespan of solutions are also given.
Keywords
, viscoelasticity, existence, blow-up, life-span, negative initial energy, positive initial energy
@article{paperid:1104619,
author = {فرامرز تهمتنی and Shahrouzi, Mohammad},
title = {Existence and blow up of solutions to a Petrovsky equation with memory and nonlinear source term},
journal = {Boundary Value Problems},
year = {2012},
volume = {2012},
number = {1},
month = {April},
issn = {1687-2770},
keywords = {viscoelasticity; existence; blow-up; life-span; negative initial energy; positive initial energy},
}
%0 Journal Article
%T Existence and blow up of solutions to a Petrovsky equation with memory and nonlinear source term
%A فرامرز تهمتنی
%A Shahrouzi, Mohammad
%J Boundary Value Problems
%@ 1687-2770
%D 2012
