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L^1 Estimate for the Dissipative Wave Equation in a Two Dimensional Exterior Domain

Kosuke Ono

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Abstract

We consider the initial-boundary value problem in a two dimensional exterior domain for the dissipative wave equation (∂2ｔ+∂- △)u= 0 with the homogeneous Dirichlet boundary condition. Using the so-called cut-off technique together with the local energy estimateand L1 and L2 estimates in the whole space，we derive the LP estimates with 1≤p≤∞ for the solution.

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We consider the initial-boundary value problem in a two dimensional exterior domain for the dissipative wave equation (∂2ｔ+∂- △)u= 0 with the homogeneous Dirichlet boundary condition. Using the so-called cut-off technique together with the local energy estimateand L1 and L2 estimates in the whole space，we derive the LP estimates with 1≤p≤∞ for the solution.

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Available abstract

We consider the initial-boundary value problem in a two dimensional exterior domain for the dissipative wave equation (∂2ｔ+∂- △)u= 0 with the homogeneous Dirichlet boundary condition. Using the so-called cut-off technique together with the local energy estimateand L1 and L2 estimates in the whole space，we derive the LP estimates with 1≤p≤∞ for the solution.

Key concepts: Dissipative system, Mathematical analysis, Mathematics, Wave equation, Domain (mathematical analysis), Boundary value problem, Dirichlet boundary condition, Homogeneous

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