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The semilinear heat equation with a Heaviside source term

Published online by Cambridge University Press:  16 July 2009

Roberto Gianni  and
Josephus Hulshof
Roberto Gianni
Affiliation:
Dipartimento di Matematica ‘Ulisse Dini’, Università di Firenze, Viale Morgagni 67/A, 50134 Firenze, Italy
Josephus Hulshof
Affiliation:
Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands
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Abstract

We consider the initial value problem for the equation ut = uxx + H(u), where H is the Heaviside graph, on a bounded interval with Dirichlet boundary conditions, and discuss existence, regularity and uniqueness of solutions and interfaces.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 3 , Issue 4 , December 1992 , pp. 367 - 379
Copyright
Copyright © Cambridge University Press 1992

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