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\(L^1\) estimates for dissipative wave equations in exterior domains. (English) Zbl 1130.35016

Exterior initial-boundary value problems for linear dissipative wave equations are investigated. Decay estimates of the solution to the Cauchy problem in the whole space and local energy estimates of higher order to the initial-boundary value problem are shown first. The \(L^1\) estimate of the solution is then obtained using the already proved estimates and the cut-off technique.

MSC:

35B40 Asymptotic behavior of solutions to PDEs
35L05 Wave equation
35L20 Initial-boundary value problems for second-order hyperbolic equations
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