Colombeau's Theory and Shock Wave Solutions for Systems of PDEs
Date
2000-03-12
Authors
Villarreal, Francisco
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
In this article we study the existence of shock wave solutions for systems of partial differential equations of hydrodynamics with viscosity in one space dimension in the context of Colombeau's theory of generalized functions. This study uses the equality in the strict sense and the association of generalized functions (that is the weak equality). The shock wave solutions are given in terms of generalized functions that have the classical Heaviside step function as macroscopic aspect. This means that solutions are sought in the form of sequences of regularizations to the Heaviside function that have to satisfy part of the equations in the strict sense and part of the equations in the sense of association.
Description
Keywords
Shock wave solution, Generalized function, Distribution
Citation
Villarreal, F. (2000). Colombeau's theory and shock wave solutions for systems of PDEs. <i>Electronic Journal of Differential Equations, 2000</i>(21), pp. 1-17.
Rights
Attribution 4.0 International