Global solutions to a class of nonlinear damped wave operator equations

Global Existence of Strong Solutions to a Class of Fully Nonlinear Wave Equations with Strongly Damped Terms

We consider the global existence of strong solution u, corresponding to a class of fully nonlinear wave equations with strongly damped terms utt −kΔut f x,Δu g x, u,Du,D2u in a bounded and smooth domain Ω in R, where f x,Δu is a given monotone in Δu nonlinearity satisfying some dissipativity and growth restrictions and g x, u,Du,D2u is in a sense subordinated to f x,Δu . By using spatial sequen...

phragmén-lindelöf type results for a class of nonlinear damped wave equations

this paper deals with the behavior at infinity of solutions to a class of wave equations with nonlinear dampingterms defined in a semi-infinite cylinder. the spatial behavior of solutions is studied and an alternative ofphragmén-lindelöf type theorems is obtained in the results. the main point in the contribution is the use of energy method.

Global Attractor for Damped Wave Equations with Nonlinear Memory

Let Ω ⊂ R be a bounded domain with a smooth boundary. We consider the longtime dynamics of a class of damped wave equations with a nonlinear memory term

On the Decay of Solutions to an Initial Boundary Value Problem for a Class of Damped Nonlinear Wave Equations

In this paper, we consider a class of strongly damped multidimensional nonlinear wave equations in a bounded domain. We show that we can always find initial data in the stable set for which the solution of the problem decays exponentially. The key tool in the proof is an idea of Zuazua [6], which is based on the construction of a suitable Lyapunov function. 2000 Mathematics Subject Classificati...

Global Existence and Asymptotic Behavior of Solutions for a Class of Nonlinear Degenerate Wave Equations