TY - JOUR
T1 - Global existence and finite time blow-up in a class of stochastic nonlinear wave equations
AU - Parshad, Rana D.
AU - Beauregard, Matthew
AU - Kasimov, Aslan
AU - Said-Houari, Belkacem
PY - 2014/1/1
Y1 - 2014/1/1
N2 - We consider a stochastic extension of a class of wave equations with nonlinear viscoelastic damping and nonlinear forcing. We show the global existence of the solution of the stochastic equation and, additionally, when the source term dominates the damping term and when the initial data are large enough, we show that the expected value of the L p norm of the solution, blows up in finite time. In the presence of noise, we extend the previously known range of initial data corresponding to blow-up. Furthermore we use a spectral stochastic Galerkin method to perform numerical simulations that verify certain special cases of our theoretical results.
AB - We consider a stochastic extension of a class of wave equations with nonlinear viscoelastic damping and nonlinear forcing. We show the global existence of the solution of the stochastic equation and, additionally, when the source term dominates the damping term and when the initial data are large enough, we show that the expected value of the L p norm of the solution, blows up in finite time. In the presence of noise, we extend the previously known range of initial data corresponding to blow-up. Furthermore we use a spectral stochastic Galerkin method to perform numerical simulations that verify certain special cases of our theoretical results.
U2 - 10.31390/cosa.8.3.07
DO - 10.31390/cosa.8.3.07
M3 - Article
JO - Faculty Publications
JF - Faculty Publications
ER -