Annali di Matematica Pura ed Applicata

, Volume 84, Issue 1, pp 309–320 | Cite as

Un problema di controllo ottimale nel cambiamento di stato in uno strato

  • Demore Quilghini


In this paper we studied a minimum property for a Stefan-like problem in a slab S. We considered all possible processes of change of state which occur under security conditions in an assigned time interval to. We proved that, among these processes the particular one for which the cooling (or warming) temperature f=f(t) is time-independent minimizes the integral\(\frac{1}{{t_o }}\int\limits_0^{t_0 } {\left| {f(t)} \right|dt}\).

As a consequence, such a process, which occurs in an asigned time interval, minimi zes the external work.


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    D. Quilghini,Una analisi Fisico-matematica del processo del cambiamento di fase, Ann. di Mat. pura ed applicata (IV), vol. LXVII, pp. 33–74 (1965).CrossRefMathSciNetGoogle Scholar
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    —— ——,Sul problema inverso di quello di Stefan, Riv. Mat. Univ. Parma (2) 8 (1967), pp. 131–142.zbMATHMathSciNetGoogle Scholar
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    -- --,Una analisi Fisico-matematica del problema di Stefan inverso in uno strato materiale piano, Istituto Matematico « U. Dini » dell'Università di Firenze (1968).Google Scholar

Copyright information

© Nicola Zanichelli Editore 1970

Authors and Affiliations

  • Demore Quilghini
    • 1
  1. 1.Firenze

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