arXiv:math/0409229 Abstract

arXiv:math/0409229 [math.AP]Abstract References Reviews Resources

Initial-Boundary Problems for Semilinear Hyperbolic Systems with Singular Coefficients

Published 2004-09-14Version 1

We use the framework of Colombeau algebras of generalized functions to study existence and uniqueness of global generalized solutions to mixed non-local problems for a semilinear hyperbolic system. Coefficients of the system as well as initial and boundary data are allowed to be strongly singular, as the Dirac delta function and derivatives thereof. To obtain the existence-uniqueness result we prove a criterion of invertibility in the full version of the Colombeau algebras.

Comments: 13 pages

Categories: math.AP

Subjects: 35L50, 35L60

Keywords: semilinear hyperbolic system, singular coefficients, initial-boundary problems, colombeau algebras, dirac delta function

Related articles: Most relevant | Search more

arXiv:2501.02951 [math.AP] (Published 2025-01-06)

Stochastic very weak solution to parabolic equations with singular coefficients

Snežana Gordić, Tijana Levajković, Ljubica Oparnica

arXiv:2001.03688 [math.AP] (Published 2020-01-10)

Revisitation of a Tartar's result on a semilinear hyperbolic system with null condition

Roberta Bianchini, Gigliola Staffilani

arXiv:0803.1012 [math.AP] (Published 2008-03-07)