Strictly dissipative boundary value problems at trihedral corners
Halpern, Laurence1 ; Rauch, Jeffrey2
1 LAGA, UMR 7539 CNRS, Université Paris 13 93430 Villetaneuse France
2 Department of Mathematics University of Michigan Ann Arbor 48109 MI USA
Séminaire Laurent Schwartz — EDP et applications (2016-2017), Exposé no. 11, 10 p.

For time independent symmetric hyperbolic systems with elliptic generators, gluing strictly dissipative boundary conditions at a multihedral corner yields a well posed boundary value problem. Uniqueness of solutions with square integrable boundary traces is proved using the Laplace transform and an H 1/2 regularity theorem.

Publié le :
DOI : 10.5802/slsedp.101
Halpern, Laurence 1 ; Rauch, Jeffrey 2

1 LAGA, UMR 7539 CNRS, Université Paris 13 93430 Villetaneuse France
2 Department of Mathematics University of Michigan Ann Arbor 48109 MI USA 
@article{SLSEDP_2016-2017____A11_0,
     author = {Halpern, Laurence and Rauch, Jeffrey},
     title = {Strictly dissipative boundary value problems at trihedral corners},
     journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
     note = {talk:11},
     pages = {1--10},
     publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {2016-2017},
     doi = {10.5802/slsedp.101},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/slsedp.101/}
}
TY  - JOUR
AU  - Halpern, Laurence
AU  - Rauch, Jeffrey
TI  - Strictly dissipative boundary value problems at trihedral corners
JO  - Séminaire Laurent Schwartz — EDP et applications
N1  - talk:11
PY  - 2016-2017
SP  - 1
EP  - 10
PB  - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
UR  - http://www.numdam.org/articles/10.5802/slsedp.101/
DO  - 10.5802/slsedp.101
LA  - en
ID  - SLSEDP_2016-2017____A11_0
ER  - 
%0 Journal Article
%A Halpern, Laurence
%A Rauch, Jeffrey
%T Strictly dissipative boundary value problems at trihedral corners
%J Séminaire Laurent Schwartz — EDP et applications
%Z talk:11
%D 2016-2017
%P 1-10
%I Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
%U http://www.numdam.org/articles/10.5802/slsedp.101/
%R 10.5802/slsedp.101
%G en
%F SLSEDP_2016-2017____A11_0
Halpern, Laurence; Rauch, Jeffrey. Strictly dissipative boundary value problems at trihedral corners. Séminaire Laurent Schwartz — EDP et applications (2016-2017), Exposé no. 11, 10 p. doi : 10.5802/slsedp.101. http://www.numdam.org/articles/10.5802/slsedp.101/

[1] K.O. Friedrichs, Symmetric hyperbolic linear differential equations. Comm. Pure Appl. Math. 7 (1954) 345-392. | DOI | MR | Zbl

[2] K.O. Friedrichs, Symmetric positive linear differential equations. Comm. Pure Appl. Math. 11 (1958) 333-418. | DOI | MR | Zbl

[3] P. Grisvard, Singularités des problèmes aux limites dans des polyèdres. (French) [Singularities of boundary value problems in polyhedra], Séminaire Goulaouic-Meyer-Schwartz, 1981/1982, exposé no. VIII, École Polytechnique, Palaiseau, 1982. | Numdam | Zbl

[4] P. Grisvard, Elliptic Problems in Nonsmooth Domains, Monographs and Studies in Mathematics, 24, Pitman Advanced Publishing Program, Boston, MA, 1985 | DOI | Zbl

[5] L. Halpern and J.R. Rauch, Bérenger/Maxwell with discontinous absorptions: existence, perfection, and no loss, Séminaire Laurent Schwartz Année 2012-2013, exposé no. X, École Polytechnique, Palaiseau, 2014. | DOI | Zbl

[6] L. Halpern and J.R. Rauch, Hyperbolic boundary value problems with trihedral corners, Discrete Contin. Dyn. Syst. 36, no. 8, 4403-4450, 2016. | DOI | MR | Zbl

[7] P. D. Lax and R. S. Phillips, Local boundary conditions for dissipative symmetric linear differential operators. Comm. Pure Appl. Math. 13 427-455, 1960. | DOI | MR | Zbl

[8] G. Métivier and J. Rauch, Strictly dissipative nonuniqueness with corners in Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics, Springer-Verlag, 2017, to appear. | DOI | Zbl

Cité par Sources :