Loss of derivatives for hyperbolic boundary problems with constant coefficients

Matthias Eller

doi:10.3934/dcdsb.2018154

Article Contents

2018, Volume 23, Issue 3: 1347-1361. Doi: 10.3934/dcdsb.2018154

This issue Previous Article Global stabilization of the Navier-Stokes-Voight and the damped nonlinear wave equations by finite number of feedback controllers Next Article

Loss of derivatives for hyperbolic boundary problems with constant coefficients

Matthias Eller

Department of Mathematics, Georgetown University, Washington, DC 20057, USA

Received: December 31, 2016

Revised: September 30, 2017

Early access: February 2018

Published: June 2018

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Abstract

Symmetric hyperbolic systems and constantly hyperbolic systems with constant coefficients and a boundary condition which satisfies a weakened form of the Kreiss-Sakamoto condition are considered. A well-posedness result is established which generalizes a theorem by Chazarain and Piriou for scalar strictly hyperbolic equations and non-characteristic boundaries [3]. The proof is based on an explicit solution of the boundary problem by means of the Fourier-Laplace transform. As long as the operator is symmetric, the boundary is allowed to be characteristic.

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Mathematics Subject Classification: Primary: 35L04; Secondary: 35L20.

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