Loss of derivatives for hyperbolic boundary problems with constant coefficients
Analysis of PDEs
2016-10-04 v1
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 from 1972. 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.
Keywords
Cite
@article{arxiv.1610.00027,
title = {Loss of derivatives for hyperbolic boundary problems with constant coefficients},
author = {Matthias Eller},
journal= {arXiv preprint arXiv:1610.00027},
year = {2016}
}