We study a quasilinear parabolic equation of forward-backward type, under assumptions on the nonlinearity which hold for a wide class of mathematical models, using a pseudo-parabolic regularization of power type.We prove existence and uniqueness of positive solutions of the regularized problem in a space of Radon measures. It is shown that these solutions satisfy suitable entropy inequalities. We also study their qualitative properties, in particular proving that the singular part of the solution with respect to the Lebesgue measure is constant in time.
Bertsch, M., Smarrazzo, F., Tesei, A. (2016). Pseudo-parabolic regularization of forward-backward parabolic equations: Power-type nonlinearities. JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK, 712, 51-80 [10.1515/crelle-2013-0123].
Pseudo-parabolic regularization of forward-backward parabolic equations: Power-type nonlinearities
BERTSCH, MICHIEL;
2016-01-01
Abstract
We study a quasilinear parabolic equation of forward-backward type, under assumptions on the nonlinearity which hold for a wide class of mathematical models, using a pseudo-parabolic regularization of power type.We prove existence and uniqueness of positive solutions of the regularized problem in a space of Radon measures. It is shown that these solutions satisfy suitable entropy inequalities. We also study their qualitative properties, in particular proving that the singular part of the solution with respect to the Lebesgue measure is constant in time.File | Dimensione | Formato | |
---|---|---|---|
Bertsch_CRELLE-2016.pdf
solo utenti autorizzati
Descrizione: articolo
Tipologia:
Versione Editoriale (PDF)
Licenza:
Copyright dell'editore
Dimensione
315.61 kB
Formato
Adobe PDF
|
315.61 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.