Energy decay rate of wave equations with indefinite damping. (English) Zbl 0960.35058

Benaddi, Ahmed; Rao, Bopeng

J. Differ. Equations 161, No. 2, 337-357 (2000).

The authors consider the one-dimensional wave equation with an indefinite sign viscous damping and a zero order potential term. The main result of the paper asserts that if the damping coefficient is “more positive than negative”, the energy of the solution of the considered equation satisfying a Dirichlet boundary condition decays uniformly exponentially to zero. This generalizes a previous result of Freitas and Zuazua. The proof is based on an asymptotic expansion of eigenvalues and eigenfunctions of the damped wave equation (established by using a shooting method).

Reviewer: C.Popa (Iaşi)

MSC:

35L20	Initial-boundary value problems for second-order hyperbolic equations
35B40	Asymptotic behavior of solutions to PDEs

Keywords:

Dirichlet boundary condition; asymptotic expansion of eigenvalues and eigenfunctions; shooting method

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