Weak solutions for equations defined by accretive operators. I
Published online by Cambridge University Press: 12 July 2007
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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