Well Posedness of Perfectly Matched or Dissipative Boundary Conditions with Trihedral Corners

Laurence Halpern (1) , Jeffrey Rauch (2)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 Department of Mathematics - University of Michigan

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 B\'erenger 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 B\'erenger split problem. Both problems have their origins in numerical methods with artificial boundaries. trihedral angle, B\'erenger's layers, strictly dissipative boundaries, symmetric hyperbolic systems, Maxwell's equations

Mots clés: Trihedral angle; Bérenger's layers; strictly dissipative boundaries; symmetric hyperbolic systems; Maxwell's equations

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Laurence Halpern, Jeffrey Rauch. Well Posedness of Perfectly Matched or Dissipative Boundary Conditions with Trihedral Corners. 2015. ⟨hal-01203481v1⟩