Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques naturelles / sciences mathematiquesVol. CXXXIII, No. 31, pp. 87–99 (2006)
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Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques naturelles / sciences mathematiques Vol. CXXXIII, No. 31, pp. 87–99 (2006) |
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Generalized solutions to singular initial-boundary hyperbolic problems with non-Lipshitz nonlinearitiesIrina KmitInstitute for Applied Problems of Mechanics and Mathematics, Ukrainian Academy of Sciences, Naukova St. 3b, 79060 Lviv, Ukraine, E-mail: kmit@ov.litech.netAbstract: We prove the existence and uniqueness of global generalized solutions in a Colombeau algebra of generalized functions to semilinear hyperbolic systems with nonlinear boundary conditions. Our analysis covers the case of non-Lipschitz nonlinearities both in the differential equations and in the boundary conditions. We admit strong singularities in the differential equations as well as in the initial and boundary conditions. Keywords: Colombeau algebra, semilinear hyperbolic system, nonlinear boundary condition Classification (MSC2000): 35L50, 35L67, 35D05 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 10 Jun 2006. This page was last modified: 20 Jun 2011.
© 2006 Mathematical Institute of the Serbian Academy of Science and Arts
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