Existence-uniqueness of strong solution to a class of quasi-linear damped wave equations with gradient term

Abstract

This work investigates global existence and uniqueness of strong solution, corresponding to a class of quasi-linear damped wave equations with gradient term in nonlinear sourcing term u tt + αu t = u + f (x,t, u, ∇u), (α > 0) in a bounded and C 2 domain Ω in R n , where f satisfying some weak growth restrictions. We obtained the global existence and uniqueness of strong solution u ∈ C 0 ((0, ∞), H 2 (Ω)) by using our previous results [1].