EMIS ELibM Electronic Journals 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 nonlinearities

Irina Kmit

Institute for Applied Problems of Mechanics and Mathematics, Ukrainian Academy of Sciences, Naukova St. 3b, 79060 Lviv, Ukraine, E-mail: kmit@ov.litech.net

Abstract: 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

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Electronic fulltext finalized on: 10 Jun 2006. This page was last modified: 20 Jun 2011.

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