Global nonexistence of solutions for a system of viscoelastic wave equations with weak damping terms
Authors :
Erhan Piskin
Author Address :
Dicle University, Department of Mathematics, 21280 Diyarbakır, Turkey.
Abstract :
This paper deals with the initial boundary value problem for the viscoelastic wave equations
egin{equation*}
left{
egin{array}{c}
u_{tt}-igtriangleup u+int
olimits_{0}^{t}g_{1}left( t- au
ight)
igtriangleup uleft( au
ight) d au +u_{t}=f_{1}left( u,v
ight) , \
v_{tt}-igtriangleup v+int
olimits_{0}^{t}g_{2}left( t- au
ight)
igtriangleup vleft( au
ight) d au +v_{t}=f_{2}left( u,v
ight)%
end{array}%
ight.
end{equation*}%
in a bounded domain. We obtain the global nonexistence of solutions by applying a lemma due to Y. Zhou [Global existence and nonexistence for a nonliear wave equation with damping and source terms, Math. Nacht, 278 (2005) 1341--1358].
Keywords :
Global nonexistence, viscoelastic wave equation.
DOI :
Article Info :
Received : June 26, 2014; Accepted : February 03, 2015.
