Exponential time decay of solutions to a nonlinear fourth-order parabolic equation

Jüngel, Ansgar; Toscani, Giuseppe

Exponential time decay of solutions to a nonlinear fourth-order parabolic equation

Dateien

preprint_139.pdfGröße: 224.34 KBDownloads: 397

Datum

2001

Autor:innen

Jüngel, Ansgar

Toscani, Giuseppe

Open Access-Veröffentlichung

Open Access Green

Sammlungen

Informatik und Informationswissenschaft

Publikationstyp

Preprint

Publikationsstatus

Published

Zusammenfassung

In this paper we investigate the large-time behavior of weak solutions to the nonlinear fourth-order parabolic equation nt = -(n(log n)xx})xx modeling interface fluctuations in spin systems. We study here the case x\in \Omega =(0,1), with n=1, nx=0 on \partial\Omega. In particular, we prove exponential decay of n(x,t) towards the constant steady state n\infty =1 in the L1 norm for long times and we give the explicit rate of decay. The result is based on classical entropy estimates and on detailed lower bounds for the entropy production.

Fachgebiet (DDC)

004 Informatik

Zitieren

ISO 690

JÜNGEL, Ansgar, Giuseppe TOSCANI, 2001. Exponential time decay of solutions to a nonlinear fourth-order parabolic equation

BibTex

@unpublished{Jungel2001Expon-5980,
  year={2001},
  title={Exponential time decay of solutions to a nonlinear fourth-order parabolic equation},
  author={Jüngel, Ansgar and Toscani, Giuseppe}
}

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