Electronic Journal of Differential Equations,
Vol. 2000(2000), No. 21, pp. 1-17.
Title: Colombeau's theory and shock wave solutions for systems of PDEs
Author: F. Villarreal (FEIS-UNESP, Sao Paulo, Brazil)
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.
Submitted January 13, 2000. Published March 12, 2000.
Math Subject Classifications: 46F99, 35G20.
Key Words: Shock wave solution; Generalized function; Distribution.