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Weak solutions for equations defined by accretive operators. I

Published online by Cambridge University Press:  12 July 2007

Manuel Portilheiro
Manuel Portilheiro
Affiliation:
University of Wisconsin-Madison, Mathematics Department, 480 Lincoln Dr, Madison, WI 53706-1388, USA
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Abstract

We propose a notion of weak solution for certain nonlinear contractive equations: ‘dissipative solution’. We show that this notion coincides with the viscosity solutions for Hamilton–Jacobi equations, as introduced by Crandall and Lions, and with the entropy solutions for conservation laws introduced by Kružkov. The proposed notion is based on the properties of accretive operators.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 133 , Issue 5 , October 2003 , pp. 1193 - 1207
Copyright
Copyright © Royal Society of Edinburgh 2003

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