We study the existence of solutions u belonging to L-1(0, T; W-0(1,1)(Omega)) boolean AND L-infinity (0, T; L-2(Omega)) of a class of nonlinear problems whose prototype is the following {u(t) - div (del u/(1+vertical bar u vertical bar(2))) = 0, in Omega(T); u - 0, on partial derivative Omega x (0,T); (1) u(x,0) = u(0)(x) is an element of L-2(Omega), in Omega. We investigate also the asymptotic estimates satisfied by distributional solutions that we find and the uniqueness.

SOME DEGENERATE PARABOLIC PROBLEMS: EXISTENCE AND DECAY PROPERTIES / Boccardo, Lucio; Porzio, Maria Michaela. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S. - ISSN 1937-1632. - STAMPA. - 7:4(2014), pp. 617-629. [10.3934/dcdss.2014.7.617]

SOME DEGENERATE PARABOLIC PROBLEMS: EXISTENCE AND DECAY PROPERTIES

BOCCARDO, Lucio;PORZIO, Maria Michaela
2014

Abstract

We study the existence of solutions u belonging to L-1(0, T; W-0(1,1)(Omega)) boolean AND L-infinity (0, T; L-2(Omega)) of a class of nonlinear problems whose prototype is the following {u(t) - div (del u/(1+vertical bar u vertical bar(2))) = 0, in Omega(T); u - 0, on partial derivative Omega x (0,T); (1) u(x,0) = u(0)(x) is an element of L-2(Omega), in Omega. We investigate also the asymptotic estimates satisfied by distributional solutions that we find and the uniqueness.
2014
decay estimates; degenerate parabolic equations; existence results; l 1(0; t; l-1(0; nonlinear parabolic problems; unbounded solutions; w-0(1; 1)(omega))-solutions; w1; 1 0 (ω)-solutions
01 Pubblicazione su rivista::01a Articolo in rivista
SOME DEGENERATE PARABOLIC PROBLEMS: EXISTENCE AND DECAY PROPERTIES / Boccardo, Lucio; Porzio, Maria Michaela. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S. - ISSN 1937-1632. - STAMPA. - 7:4(2014), pp. 617-629. [10.3934/dcdss.2014.7.617]
File allegati a questo prodotto
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/559718
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 11
  • ???jsp.display-item.citation.isi??? 7
social impact