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Existence and uniqueness of solutions to a concentrated capacity problem with change of phase

Published online by Cambridge University Press:  16 July 2009

Daniele Andreucci
Daniele Andreucci
Affiliation:
Università di Firenze, Dipartimento di Matematica U. Dini, v.le Morgagni 67/A, 50134 Firenze, Italy
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Abstract

A concentrated capacity problem is posed for the heat equation in a multidimensional domain. In the concentrated capacity (i.e. in a portion of the boundary of the domain) a change of phase takes place, and a Stefan-like problem is posed. This scheme has been introduced in the literature as the formal limiting case of a certain class of diffusion problems.

Our main result is a theorem of continuous dependence of the solution on the data. It is also used to prove the existence of the solution (in a weak sense), assuming only integrability of the data. The solution is found as the limit of the solutions of the approximating problems.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 1 , Issue 4 , December 1990 , pp. 339 - 351
Copyright
Copyright © Cambridge University Press 1990

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