Global existence and blow-up of solutions for a system of nonlinear viscoelastic wave equations with damping and source ☆

@article{Han2009GlobalEA,
  title={Global existence and blow-up of solutions for a system of nonlinear viscoelastic wave equations with damping and source ☆},
  author={Xiaosen Han and M. Wang},
  journal={Nonlinear Analysis-theory Methods & Applications},
  year={2009},
  volume={71},
  pages={5427-5450}
}
  • Xiaosen Han, M. Wang
  • Published 2009
  • Mathematics
  • Nonlinear Analysis-theory Methods & Applications
  • Abstract In this paper we investigate the global existence and finite time blow-up of solutions to the system of nonlinear viscoelastic wave equations u t t − Δ u + ∫ 0 t g 1 ( t − τ ) Δ u ( τ ) d τ + | u t | m − 1 u t = f 1 ( u , v ) , v t t − Δ v + ∫ 0 t g 2 ( t − τ ) Δ v ( τ ) d τ + | v t | r − 1 v t = f 2 ( u , v ) in Ω × ( 0 , T ) with initial and Dirichlet boundary conditions, where Ω is a bounded domain in R n , n = 1 , 2 , 3 . Under suitable assumptions on the functions g i ( ⋅ ) , f i… CONTINUE READING
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