2012 / December Volume 7 No.4
Dirichlet-Neumann Kernel for Hyperbolic-Dissipative System in Half-Space
Published Date |
2012 / December
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Title | Dirichlet-Neumann Kernel for Hyperbolic-Dissipative System in Half-Space |
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Pagination | 477-543 |
Abstract | The purpose of the present paper is to initiate a systematic study of
the relation of the boundary values for hyperbolic-dissipative
systems of partial differential equations. We introduce a general
framework for explicitly deriving the boundary kernel for the
Dirichlet-Neumann map. We first use the Laplace and Fourier
transforms, and the stability consideration to derive the Master
Relationship, the Dirichlet-Neumann relation in the transformed
variables. New idea of Fourier-Laplace path and algebraic
considerations are introduced for the explicit inversion of
Fourier-Laplace transforms. We illustrate the basic ideas by
carrying out the framework to models in the gas dynamics and the
dissipative wave equations.
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AMS Subject Classification |
35G10, 35C05
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Received |
2012-11-09
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Accepted |
2012-12-10
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