Open Access
Translator Disclaimer
July 2003 Generalized solutions in the Egorov formulation of nonlinear diffusion equations and linear hyperbolic equations in the Colombeau algebra
Hideo Deguchi
Hiroshima Math. J. 33(2): 197-216 (July 2003). DOI: 10.32917/hmj/1150997946

Abstract

We investigate generalized solutions of nonlinear diffusion equations and linear hyperbolic equations with discontinuous coefficients in the framework of Colombeau’s algebra of generalized functions. Under Egorov’s formulation, we obtain results on existence and uniqueness of generalized solutions, which are shown to be consistent with classical solutions. The example of a linear hyperbolic equation given by Hurd and Sattinger [8] has no distributional solutions in Schwartz’s sense, but has the unique generalized solution. We study what distribution is associated with it, namely, how it behaves on the level of information of distribution theory.

Citation

Download Citation

Hideo Deguchi. "Generalized solutions in the Egorov formulation of nonlinear diffusion equations and linear hyperbolic equations in the Colombeau algebra." Hiroshima Math. J. 33 (2) 197 - 216, July 2003. https://doi.org/10.32917/hmj/1150997946

Information

Published: July 2003
First available in Project Euclid: 22 June 2006

zbMATH: 1047.35033
MathSciNet: MR1997694
Digital Object Identifier: 10.32917/hmj/1150997946

Subjects:
Primary: 35K57
Secondary: 35D05, 35R05, 46F30

Rights: Copyright © 2003 Hiroshima University, Mathematics Program

JOURNAL ARTICLE
20 PAGES


SHARE
Vol.33 • No. 2 • July 2003
Back to Top