JournalszaaVol. 21, No. 3pp. 669–680

Exact Solution of a System of Generalized Hopf Equations

  • K.T. Joseph

    Tata Institute of Fundamental Research, Mumbai, India
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Abstract

In this paper we construct explicit solutions for initial value problem for a system of first order equations. When n=1n = 1, this system is just the standard Hopf equation in conservative form. When n>1n > 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