International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 6, Pages 369-382
doi:10.1155/S0161171200000971

On the existence of solutions of strongly damped nonlinear wave equations

Jong Yeoul Park and Jeong Ja Bae

Department of Mathematics, Pusan National University, Pusan 609-735, Korea

Received 18 June 1998

Copyright © 2000 Jong Yeoul Park and Jeong Ja Bae. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We investigate the existence and uniqueness of solutions of the following equation of hyperbolic type with a strong dissipation: utt(t,x)−(α+β(∫Ω|∇u(t,y)|2dy)γ)Δu(t,x)                                −λΔut(t,x)+μ|u(t,x)|q−1u(t,x)=0,     x∈Ω,t≥0            u(0,x)=u0(x),          ut(0,x)=u1(x),      x∈Ω,  u|∂Ω=0, where q>1,λ>0,μ∈ℝ,α,β≥0,α+β>0, and Δ is the Laplacian in ℝN.