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 utt +αut =4u+ f (x, t,u,∇u),(α > 0) in a bounded and C2 domain Ω in Rn, where f satisfying some weak growth restrictions. We obtained the global existence and uniqueness of strong solution u ∈C0((0,∞),H2(Ω)) by using our previous results [1].