Energy estimate for a linear symmetric       hyperbolic-parabolic system in half line

Tohru Nakamura; Shinya Nishibata

doi:10.3934/krm.2013.6.883

Article Contents

2013, Volume 6, Issue 4: 883-892. Doi: 10.3934/krm.2013.6.883

This issue Previous Article Nonlinear stability of Broadwell model with Maxwell diffuse boundary condition Next Article The Cauchy problem for the Vlasov-Dirac-Benney equation and related issues in fluid mechanics and semi-classical limits

Energy estimate for a linear symmetric hyperbolic-parabolic system in half line

Tohru Nakamura^1, and
Shinya Nishibata^2,

1.
Faculty of Mathematics, Kyushu University, Fukuoka 819-0395
2.
Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo 152-8552

Received: August 2013

Revised: September 2013

Published: December 2013

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Abstract

In the present paper, we study the initial boundary value problem for a linear symmetric hyperbolic-parabolic system in one-dimensional half space. We obtain a priori estimates by using an energy method developed by Matsumura--Nishida for half space problem under the assumption that a stability condition of Shizuta--Kawashima type holds. The method developed in the present paper is applicable to showing the nonlinear stability of boundary layer solutions for a system of viscous conservation laws in half space.

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Mathematics Subject Classification: Primary: 35B35, 76N15; Secondary: 35B40.

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References

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