Generalized Solutions to Hyperbolic Systems with Nonlinear Conditions and Strongly Singular Data

Details Generalized Solutions to Hyperbolic Systems with Nonlinear Conditions and Strongly Singular Data Generalized Solutions to Hyperbolic Systems with Nonlinear Conditions and Strongly Singular Data

2005-04-05

arxiv.org/abs/math/0504076v1

Mathematics

Analysis of PDEs

18 pages

Scientific paper

Using the framework of Colombeau algebras of generalized functions, we prove the existence and uniqueness results for global generalized solvability of semilinear hyperbolic systems with nonlinear nonlocal boundary conditions. We admit strong singularities in the differential equations as well as in the initial and boundary conditions. Our analysis covers the case of non-Lipshitz nonlinearities both in the differential equations and in the boundary conditions.

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