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

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2001

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Jüngel, Ansgar
Toscani, Giuseppe

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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.

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ISO 690JÜNGEL, 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@unpublished{Jungel2001Expon-5980,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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