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A dynamic domain decomposition for the eikonal-diffusion equation
Hyperbolic equations of Von Karman type
1. | Département de Mathématiques, UPMC (Paris VI), Paris, France |
2. | Department of Mathematics, University of Wisconsin, Milwaukee, WI 53201, United States |
References:
[1] |
M. S. Berger, On von Karman's equations and the buckling of a thin elastic plate, Comm. Pure App. Math., 20 (1967), 687-719.
doi: 10.1002/cpa.3160200405. |
[2] |
P. Cherrier and A. Milani, Equations of von Karman type on compact Kähler manifolds, Bull. Sc. Math., 2e série, 116 (1992), 325-352. |
[3] |
P. Cherrier and A. Milani, Parabolic equations of von Karman type on Kähler manifolds, Bull. Sc. Math., 131 (2007), 375-396.
doi: 10.1016/j.bulsci.2006.05.008. |
[4] |
P. Cherrier and A. Milani, Hyperbolic equations of von Karman type on Kähler manifolds, Bull. Sc. Math., 136 (2012), 19-36.
doi: 10.1016/j.bulsci.2011.07.017. |
[5] |
P. Cherrier and A. Milani, Linear and Quasi-Linear Evolution Equations in Hilbert Spaces, GSM vol. 35, American Mathematical Society, Providence, RI 2012. |
[6] |
P. Cherrier and A. Milani, Evolution Equations of von Karman Type, To appear in the Lecture Notes of the Unione Matematica Italiana, {17}, 2015.
doi: 10.1007/978-3-319-20997-5. |
[7] |
I. Chuesov and I. Lasiecka, Von Karman Evolution Equations: Well-Posedness and Long-Time Dynamics, Springer-Verlag, New York, 2010.
doi: 10.1007/978-0-387-87712-9. |
[8] |
A. Favini, M. A. Horn, I. Lasiecka, and D. Tataru, Global existence of solutions to a von Karman system with nonlinear boundary dissipation, J. Diff. Int. Eqs., 9 (1996), 267-294. |
[9] |
A. Favini, M. A. Horn, I. Lasiecka, and D. Tataru, Addendum to the paper "Global existence of solutions to a von Karman system with nonlinear boundary dissipation'', J. Diff. Int. Eqs., 10 (1997), 197-200. |
[10] |
J. L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires, Dunod - Gauthier-Villars, Paris, 1969. |
[11] |
J. L. Lions and E. Magenes, Non-Homogeneous Boundary value Problems, Vol. I, Springer Verlag, New York, 1972. |
[12] |
A. Majda, Compressible Fluid Flows and Systems of Conservation Laws in Several Space Variables, Springer-Verlag, New York, 1984.
doi: 10.1007/978-1-4612-1116-7. |
[13] |
Y. Shizuta, Strong continuity in time of the solution of the mixed problem for symmetric hyperbolic systems, Nonlinear Anal., T.M.A., 30 (1997), 2517-2524.
doi: 10.1016/S0362-546X(97)00314-3. |
show all references
References:
[1] |
M. S. Berger, On von Karman's equations and the buckling of a thin elastic plate, Comm. Pure App. Math., 20 (1967), 687-719.
doi: 10.1002/cpa.3160200405. |
[2] |
P. Cherrier and A. Milani, Equations of von Karman type on compact Kähler manifolds, Bull. Sc. Math., 2e série, 116 (1992), 325-352. |
[3] |
P. Cherrier and A. Milani, Parabolic equations of von Karman type on Kähler manifolds, Bull. Sc. Math., 131 (2007), 375-396.
doi: 10.1016/j.bulsci.2006.05.008. |
[4] |
P. Cherrier and A. Milani, Hyperbolic equations of von Karman type on Kähler manifolds, Bull. Sc. Math., 136 (2012), 19-36.
doi: 10.1016/j.bulsci.2011.07.017. |
[5] |
P. Cherrier and A. Milani, Linear and Quasi-Linear Evolution Equations in Hilbert Spaces, GSM vol. 35, American Mathematical Society, Providence, RI 2012. |
[6] |
P. Cherrier and A. Milani, Evolution Equations of von Karman Type, To appear in the Lecture Notes of the Unione Matematica Italiana, {17}, 2015.
doi: 10.1007/978-3-319-20997-5. |
[7] |
I. Chuesov and I. Lasiecka, Von Karman Evolution Equations: Well-Posedness and Long-Time Dynamics, Springer-Verlag, New York, 2010.
doi: 10.1007/978-0-387-87712-9. |
[8] |
A. Favini, M. A. Horn, I. Lasiecka, and D. Tataru, Global existence of solutions to a von Karman system with nonlinear boundary dissipation, J. Diff. Int. Eqs., 9 (1996), 267-294. |
[9] |
A. Favini, M. A. Horn, I. Lasiecka, and D. Tataru, Addendum to the paper "Global existence of solutions to a von Karman system with nonlinear boundary dissipation'', J. Diff. Int. Eqs., 10 (1997), 197-200. |
[10] |
J. L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires, Dunod - Gauthier-Villars, Paris, 1969. |
[11] |
J. L. Lions and E. Magenes, Non-Homogeneous Boundary value Problems, Vol. I, Springer Verlag, New York, 1972. |
[12] |
A. Majda, Compressible Fluid Flows and Systems of Conservation Laws in Several Space Variables, Springer-Verlag, New York, 1984.
doi: 10.1007/978-1-4612-1116-7. |
[13] |
Y. Shizuta, Strong continuity in time of the solution of the mixed problem for symmetric hyperbolic systems, Nonlinear Anal., T.M.A., 30 (1997), 2517-2524.
doi: 10.1016/S0362-546X(97)00314-3. |
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