On the moments of solutions to linear parabolic equations involving the biharmonic operator

Filippo Gazzola

doi:10.3934/dcds.2013.33.3583

Article Contents

2013, Volume 33, Issue 8: 3583-3597. Doi: 10.3934/dcds.2013.33.3583

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On the moments of solutions to linear parabolic equations involving the biharmonic operator

Filippo Gazzola^1,

1.
Dipartimento di Matematica del Politecnico, Piazza L. da Vinci 32, Milano, 20133

Received: May 31, 2012

Revised: July 31, 2012

Published: July 2013

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Abstract

We consider the solutions to Cauchy problems for the parabolic equation $u_\tau +\Delta^2u=0$ in $\mathbb{R}_+\times\mathbb{R}^n$, with fast decay initial data. We study the behavior of their moments. This enables us to give a more precise description of the sign-changing behavior of solutions corresponding to positive initial data.

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Mathematics Subject Classification: 35K30.

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