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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

## Abstract

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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Additional Information: | 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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