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Finite speed of propagation for mixed problems in the $WR$ class
1. | Université de Nantes, Laboratoire de Mathématiques Jean Leray (CNRS UMR6629), 2 rue de la Houssinière, BP 92208, 44322 Nantes Cedex 3, France |
References:
[1] |
S. Benzoni-Gavage, F. Rousset, D. Serre and K. Zumbrun, Generic types and transitions in hyperbolic initial-boundary-value problems, Proc. Roy. Soc. Edinburgh Sect. A, 5 (2002), 1073-1104.
doi: 10.1017/S030821050000202X. |
[2] |
S. Benzoni-Gavage and D. Serre, Multidimensional Hyperbolic Partial Differential Equations, Oxford Mathematical Monographs, Oxford University Press, 2007. |
[3] |
A. Chazarain and J. Piriou, Caractérisation des problèmes mixtes hyperboliques bien posés differentiables, (French) [Characterization of well-posed mixed hyperbolic mixed problems.], Ann. Inst. Fourier (Grenoble), 22 (1972), 193-237. |
[4] |
A. Chazarain and J. Piriou, Introduction à la théorie des équations aux dérivées partielles linéaires,, (French) [Introduction to the theory of linear partial differential equations.], ().
|
[5] |
J.-F. Coulombel, Well-posedness of hyperbolic initial boundary value problems, J. Math. Pures Appl., 84 (2005), 786-818.
doi: 10.1016/j.matpur.2004.10.005. |
[6] |
J.-F. Coulombel and O. Guès, Geometric optics expansions with amplification for hyperbolic boundary value problems: linear problems, Ann. Inst. Fourier (Grenoble), 60 (2010), 2183-2233. |
[7] |
M. Ikawa, Mixed problem for the wave equation with an oblique derivative boundary condition, Osaka J. Math., 7 (1970), 495-525. |
[8] |
H.-O. Kreiss, Initial boundary value problems for hyperbolic systems, Comm. Pure Appl. Math., 23 (1970), 277-298. |
[9] |
G. Métivier, The block structure condition for symmetric hyperbolic systems, Bull. London Math. Soc., 32 (2000), 689-702.
doi: 10.1112/S0024609300007517. |
[10] |
A. Morando and P. Secchi, Regularity of weakly well posed hyperbolic mixed problems with characteristic boundary, J. Hyperbolic Differ. Equ., 8 (2011), 37-99.
doi: 10.1142/S021989161100238X. |
[11] |
J. Rauch, Hyperbolic Partial Differential Equations and Geometric Optics, American Mathematical Society, Providence, RI, 2012. |
[12] |
M. Sablé-Tougeron, Existence pour un problème de l'élastodynamique Neumann non linéaire en dimension $2$, (French) [Existence for a non-linear elastodynamic Neumann problem in $2$ dimensions], Arch. Rational Mech. Anal., 101 (1988), 261-292.
doi: 10.1007/BF00253123. |
[13] |
T. Shirota, On the propagation speed of hyperbolic operator with mixed boundary conditions, J. Fac. Sci. Hokkaido Univ. Ser. I, 22 (1972), 25-31. |
show all references
References:
[1] |
S. Benzoni-Gavage, F. Rousset, D. Serre and K. Zumbrun, Generic types and transitions in hyperbolic initial-boundary-value problems, Proc. Roy. Soc. Edinburgh Sect. A, 5 (2002), 1073-1104.
doi: 10.1017/S030821050000202X. |
[2] |
S. Benzoni-Gavage and D. Serre, Multidimensional Hyperbolic Partial Differential Equations, Oxford Mathematical Monographs, Oxford University Press, 2007. |
[3] |
A. Chazarain and J. Piriou, Caractérisation des problèmes mixtes hyperboliques bien posés differentiables, (French) [Characterization of well-posed mixed hyperbolic mixed problems.], Ann. Inst. Fourier (Grenoble), 22 (1972), 193-237. |
[4] |
A. Chazarain and J. Piriou, Introduction à la théorie des équations aux dérivées partielles linéaires,, (French) [Introduction to the theory of linear partial differential equations.], ().
|
[5] |
J.-F. Coulombel, Well-posedness of hyperbolic initial boundary value problems, J. Math. Pures Appl., 84 (2005), 786-818.
doi: 10.1016/j.matpur.2004.10.005. |
[6] |
J.-F. Coulombel and O. Guès, Geometric optics expansions with amplification for hyperbolic boundary value problems: linear problems, Ann. Inst. Fourier (Grenoble), 60 (2010), 2183-2233. |
[7] |
M. Ikawa, Mixed problem for the wave equation with an oblique derivative boundary condition, Osaka J. Math., 7 (1970), 495-525. |
[8] |
H.-O. Kreiss, Initial boundary value problems for hyperbolic systems, Comm. Pure Appl. Math., 23 (1970), 277-298. |
[9] |
G. Métivier, The block structure condition for symmetric hyperbolic systems, Bull. London Math. Soc., 32 (2000), 689-702.
doi: 10.1112/S0024609300007517. |
[10] |
A. Morando and P. Secchi, Regularity of weakly well posed hyperbolic mixed problems with characteristic boundary, J. Hyperbolic Differ. Equ., 8 (2011), 37-99.
doi: 10.1142/S021989161100238X. |
[11] |
J. Rauch, Hyperbolic Partial Differential Equations and Geometric Optics, American Mathematical Society, Providence, RI, 2012. |
[12] |
M. Sablé-Tougeron, Existence pour un problème de l'élastodynamique Neumann non linéaire en dimension $2$, (French) [Existence for a non-linear elastodynamic Neumann problem in $2$ dimensions], Arch. Rational Mech. Anal., 101 (1988), 261-292.
doi: 10.1007/BF00253123. |
[13] |
T. Shirota, On the propagation speed of hyperbolic operator with mixed boundary conditions, J. Fac. Sci. Hokkaido Univ. Ser. I, 22 (1972), 25-31. |
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