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Vietnam Journal of Mathematics 34:3(2006) 295-305

 Global Existence of Solution for Semilinear Dissipative Wave Equation

MD. Abu Naim Sheikh and MD. Abdul Matin

Abstract.  In this paper, we consider an initial--boundary value problem for the semilinear dissipative wave equation in one space dimension of the type :

utt uxx + |u|m-1ut = V(t)|u|m-1u + f(t, x) in (0, ) x (a, b),

where initial data u(0, x) = u0(x) H01(a, b), ut(0, x) = u1(x) L2(a, b) and boundary condition u(t, a) = u(t, b) = 0 for t > 0 with m > 1, on a bounded interval (a, b). The potential function V(t) is smooth, positive and the source f(t, x) is bounded. We investigate the global existence of solution as t -> ∞ under certain assumptions on the functions V(t) and f(t, x).

2000 Mathematics Subject Classification: 35B40, 35L70.

Keywords: Global existence, semilinear dissipative wave equation, nonlinear damping, potential function, source function.

 

 

 

 

 

 

 

 

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