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Blow-up time involved with perturbed Hamilton–Jacobi equations

Published online by Cambridge University Press:  14 November 2011

G. Díaz
G. Díaz
Affiliation:
Departamento de Matemática Aplicada, Universidad Complutense de Madrid, 28040-Madrid, Spain
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Synopsis

In this paper we consider the evolution of positive bounded uniformly continuous data u0 by perturbed equations like

Under general assumptions on u0, existence, uniqueness and regularity of the evolution u in the set

are studied, where the blow-up function is given by .

The exact blow-up rate of u is obtained. Uniqueness, regularity, decay at infinity of the function , as well a s a representation formula for the case m = 1, are also proved.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 122 , Issue 1-2 , 1992 , pp. 17 - 44
Copyright
Copyright © Royal Society of Edinburgh 1992

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