Dirichlet-Neumann Kernel for Hyperbolic-Dissipative System in Half-Space
by Tai-Ping Liu   Shih-Hsien Yu  

Vol. 7 No. 4 (2012) P.477~P.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.

KEYWORDS
Hyperbolic-dissipative systems, Boundary relations, Laplace-Fourier path

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 35G10, 35C05

MILESTONES

Received: 2012-11-09
Revised :
Accepted: 2012-12-10

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