Geodesic
On the Cauchy problem for a class of parabolic equations with variable density
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 9 (1998) no. 4, pp. 279-298

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

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. 
@article{RLIN_1998_9_9_4_a4,
     author = {Kamin, Shoshana and Kersner, Robert and Tesei, Alberto},
     title = {On the {Cauchy} problem for a class of parabolic equations with variable density},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {279--298},
     publisher = {mathdoc},
     volume = {Ser. 9, 9},
     number = {4},
     year = {1998},
     zbl = {0926.35045},
     mrnumber = {MR1722787},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_1998_9_9_4_a4/}
}
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Kamin, Shoshana; Kersner, Robert; Tesei, Alberto. On the Cauchy problem for a class of parabolic equations with variable density. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 9 (1998) no. 4, pp. 279-298. http://geodesic.mathdoc.fr/item/RLIN_1998_9_9_4_a4/