Global existence and asymptotic behaviour of solution for a damped nonlinear hyperbolic equation. (September 2020) - Pang, Tiantian; Shen, Jihong
Abstract: In this paper we study the initial–boundary value problem for a damped nonlinear hyperbolic equation u t t + Δ 2 u + α Δ 2 u t + Δ f ( Δ u ) = 0, x ∈ Ω, t > 0, u ( x, 0 ) = u 0 ( x ), u t ( x, 0 ) = u 1 ( x ), x ∈ Ω, u = 0 Δ u = 0, x ∈ ∂ Ω, t ≥ 0, where Ω ⊂ R n, n ≥ 1 and α is a positive constant. Under some assumptions on f ( s ) and initial data, we prove the global existence of solution. Furthermore, we prove that the solution decays to zero exponentially.