Finite Speed of Propagation and Waiting Time for Local Solutions of Degenerate Equations in Viscoelastic Media or Heat Flows with Memory

被引：0
|
作者：
Antontsev S.N. [1 ,2 ,3 ]
Díaz J.I. [4 ]
机构：
[1] M.A. Lavrentyev Institute of Hydrodynamics SB RAS, Novosibirsk
[2] Novosibirsk State University, Novosibirsk
[3] CMAF-CIO, University of Lisbon, Lisbon
[4] Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid
来源：
Journal of Elliptic and Parabolic Equations | 2016年 / 2卷 / 1-2期
基金：
俄罗斯科学基金会;
关键词：
35K92; 45K05; finite speed of propagation; heat flows with memory; non-linear viscoelastic equation; Nonlocal equation; waiting time property;
D O I：
10.1007/BF03377402
中图分类号：
学科分类号：
摘要：
The finite speed of propagation (FSP) was established for certain materials in the 70’s by the American school (Gurtin, Dafermos, Nohel, etc.) for the special case of the presence of memory effects. A different approach can be applied by the construction of suitable super and sub-solutions (Crandall, Nohel, Díaz and Gomez, etc.). In this paper we present an alternative method to prove (FSP) which only uses some energy estimates and without any information coming from the characteristics analysis. The waiting time property is proved for the first time in the literature for this class of nonlocal equations. © 2016, Orthogonal Publishing and Springer International Publishing.
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页码：207 / 216
页数：9
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