Hausdorff continuous solutions of conservation laws

Autor:	J. H. van der Walt, Dennis Ferdinand Agbebaku, Roumen Anguelov
Rok vydání:	2012
Předmět:	Conservation law Uniform convergence Mathematical analysis Hausdorff space Initial value problem Applied mathematics Urysohn and completely Hausdorff spaces Continuous functions on a compact Hausdorff space Entropy (arrow of time) Subspace topology Mathematics
Zdroj:	AIP Conference Proceedings.
ISSN:	0094-243X
DOI:	10.1063/1.4758953
Popis:	We present a framework for studying discontinuous solutions of the Cauchy problem for nonlinear conservation laws, in particular entropy solutions of scalar conservation laws. The space of generalized solutions is constructed as the completion of the space of continuously differentiable functions with respect to a suitable uniform convergence structure. Within this context the well-posedness of the problem follows in an easy and natural way. Furthermore, we show that the space of solutions is a subspace of the space of Hausdorff continuous interval valued functions which improves significantly on the current regularity results of the entropy solution.
Databáze:	OpenAIRE
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