On the Cauchy problem for a class of parabolic equations with variable density

Kamin, Shoshana ; Kersner, Robert ; Tesei, Alberto

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 9 (1998), p. 279-298 / Harvested from Biblioteca Digitale Italiana di Matematica

Abstract

The well-posedness of the Cauchy problem for a class of parabolic equations with variable density is investigated. Necessary and sufficient conditions for existence and uniqueness in the class of bounded solutions are proved. If these conditions fail, sufficient conditions are given to ensure well-posedness in the class of bounded solutions which satisfy suitable constraints at infinity.

Résumé

Si studia la buona posizione del problema di Cauchy per una classe di equazioni paraboliche con densità variabile. Si ricavano condizioni necessarie e sufficienti per l’esistenza e l’unicità nella classe delle soluzioni limitate. Se tali condizioni non sono verificate, si danno condizioni sufficienti a garantire la buona posizione del problema nella classe delle soluzioni limitate che all’infinito soddisfano opportune restrizioni.

Détail

Publié le : 1998-12-01

MR 1722787 | Zbl 0926.35045

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