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Zeitschrift für Analysis und ihre Anwendungen


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Volume 21, Issue 3, 2002, pp. 669–680
DOI: 10.4171/ZAA/1101

Published online: 2002-09-30

Exact Solution of a System of Generalized Hopf Equations

K.T. Joseph[1]

(1) Tata Institute of Fundamental Research, Mumbai, India

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.

Keywords: Generalized Hopf equations, Hopf-Cole transformation, explicit formula for the solutions of generalized Hopf equations

Joseph K.T.: Exact Solution of a System of Generalized Hopf Equations. Z. Anal. Anwend. 21 (2002), 669-680. doi: 10.4171/ZAA/1101