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 $\partial_t+\Delta^2$ 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.
Ferrero, A., Gazzola, F., & Grunau HC (2008). Decay and eventual local positivity for biharmonic parabolic equations. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S, 21(4), 1129-1157.
Citazione: | Ferrero, A., Gazzola, F., & Grunau HC (2008). Decay and eventual local positivity for biharmonic parabolic equations. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S, 21(4), 1129-1157. |
Tipo: | Articolo in rivista - Articolo scientifico |
Carattere della pubblicazione: | Scientifica |
Titolo: | Decay and eventual local positivity for biharmonic parabolic equations |
Autori: | Ferrero, A; Gazzola, F; Grunau HC |
Autori: | |
Data di pubblicazione: | 2008 |
Lingua: | English |
Rivista: | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S |
Appare nelle tipologie: | 01 - Articolo su rivista |