Decay and eventual local positivity for biharmonic parabolic equations

Alberto Ferrero, Filippo Gazzola, Hans Christoph Grunau

Risultato della ricerca: Contributo su rivistaArticolo in rivistapeer review

Abstract

We study existence and positivity properties for solutions of Cauchy problems for both linear and semilinear parabolic equations with the biharmonic operator as elliptic principal part. The self-similar kernel of the parabolic operator dt + Δ2 is a sign changing function and the solution of the evolution problem with a positive initial datum may display almost instantaneous change of sign. We determine conditions on the initial datum for which the corresponding solution exhibits some kind of positivity behaviour. We prove eventual local positivity properties both in the linear and semilinear case. At the same time, we show that negativity of the solution may occur also for arbitrarily large given time, provided the initial datum is suitably constructed.

Lingua originaleInglese
pagine (da-a)1129-1167
Numero di pagine39
RivistaDiscrete and Continuous Dynamical Systems
Volume21
Numero di pubblicazione4
Stato di pubblicazionePubblicato - ago 2008
Pubblicato esternamente

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