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On the growth of the interfaces of a nonlinear degenerate parabolic equation



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Herrero, Miguel A. (1983) On the growth of the interfaces of a nonlinear degenerate parabolic equation. In Contributions to nonlinear partial differential equations. Research notes in mathematics (89). Pitman, Boston, pp. 218-224. ISBN 0-273-08595-6


The author deals with the propagation of the support of the initial function in the following problem: ut−(um)xx+cun=0 on R×(0,+∞), u(x,0)=u0(x) on R with n≥m>1, c>0; u0 is bounded and has bounded support, and u0≥0. The author proves the following result: If u is a generalized solution to the above problem and ζ(t)=sup{x∈R: u(t,x)>0} then for n=m, ζ(t)≤ζ(2)+Alnt; and for m<n<m+2,ζ(t)≤ζ(2)+Btβ. A similar result holds for ζ(t)=inf{x∈R: u(t,x)>0}.

Item Type:Book Section
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Proceedings of the international meeting on nonlinear partial differential equations held in Madrid, December 14–17, 1981

Uncontrolled Keywords:Growth of the interfaces; large time behaviour; Cauchy problem
Subjects:Sciences > Mathematics > Differential equations
ID Code:22739
Deposited On:09 Sep 2013 15:48
Last Modified:12 Dec 2018 15:08

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