# Exact Solution of a System of Generalized Hopf Equations

### K.T. Joseph

Tata Institute of Fundamental Research, Mumbai, India

## Abstract

In this paper we construct explicit solutions for initial value problem for a system of first order equations. When $n=1$, this system is just the standard Hopf equation in conservative form. When $n>1$, the system is non-conservative. We use the vanishing viscosity method to construct solutions. As the system is non-conservative we use Volpert product and the algebra of generalized Colombeau functions to make sense of the products which appear in the equations.

## Cite this article

K.T. Joseph, Exact Solution of a System of Generalized Hopf Equations. Z. Anal. Anwend. 21 (2002), no. 3, pp. 669–680

DOI 10.4171/ZAA/1101