The initial–boundary value problems for a class of nonlinear wave equations with damping term

Abstract

In this paper we study the existence and uniqueness of the global generalized solution and the global classical solution, the blowup of the solution and the energy decay of the solutions of the initial-boundary value problems for a class of nonlinear wave equations.

Initial boundary value problem for a class of fourth-order wave equation with viscous damping term

“…Most recently, Chen and Lu [5] studied problem (1.1)-(1.3). They proved the existence of global strong solution under the assumption f 0 (s) !…”

“…f 1 (s) ¼ as 2kþ1 , satisfies the assumption f 0 (s) ! C 0 addressed in [5]. And the global well-posedness for the other cases f(s) ¼ f i (s) (i ¼ 2, 3,4) are left open.…”

“…And the global well-posedness for the other cases f(s) ¼ f i (s) (i ¼ 2, 3,4) are left open. In addition, as pointed in [5], they only treated the global nonexistence for E(0) a 0 < 0. And the case E(0) !…”

Local existence and global nonexistence theorems for a damped nonlinear hyperbolic equation

“…(See [9].) Assume that w(t) ∈ C [0, ∞) ∩ C 2 (0, ∞), and satisfies the following ordinary differential inequalitÿ…”

Blow‐up phenomena for a class of fourth‐order nonlinear wave equations with a viscous damping term

“…This problem is also studied with other boundary conditions in . Because of the propagating of the wave in the medium with the dispersion effect, Chen and Lu studied the Equation which is the nonlinear wave equation with a viscous damping term. They proved that the problem admits a unique global generalized solution provided that f ′( s ) is bounded blow.…”