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

2005/04/05 by Irina Kmit, Kmit, Irina · 1 citation
Mathematics · #Mathematical and Theoretical Analysis #Probability and Statistical Research #Mathematical Analysis and Transform Methods

paper · doi:10.48550/arxiv.math/0504076

Abstract

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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• Generalized functions as a tool for nonsmooth nonlinear problems in mathematics and physics

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