# American Institute of Mathematical Sciences

August  2016, 36(8): 4403-4450. doi: 10.3934/dcds.2016.36.4403

## Hyperbolic boundary value problems with trihedral corners

 1 Université Paris 13, CNRS, UMR 7539 LAGA, 99 av. Jean-Baptiste Clément, F-93430 Villetaneuse 2 Department of Mathematics, University of Michigan, Ann Arbor, Michigan

Received  May 2015 Revised  December 2015 Published  March 2016

Existence and uniqueness theorems are proved for boundary value problems with trihedral corners and distinct boundary conditions on the faces. Part I treats strictly dissipative boundary conditions for symmetric hyperbolic systems with elliptic or hidden elliptic generators. Part II treats the Bérenger split Maxwell equations in three dimensions with possibly discontinuous absorptions. The discontinuity set of the absorptions or their derivatives has trihedral corners. Surprisingly, there is almost no loss of derivatives for the Bérenger split problem. Both problems have their origins in numerical methods with artificial boundaries.
Citation: Laurence Halpern, Jeffrey Rauch. Hyperbolic boundary value problems with trihedral corners. Discrete & Continuous Dynamical Systems - A, 2016, 36 (8) : 4403-4450. doi: 10.3934/dcds.2016.36.4403
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