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

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Abstract

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.

2010 Mathematics Subject Classication

35K92 45K05 

Key words and phrases

Nonlocal equation non-linear viscoelastic equation finite speed of propagation waiting time property heat flows with memory 

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Copyright information

© Orthogonal Publishing and Springer International Publishing 2016

Authors and Affiliations

  1. 1.M.A. Lavrentyev Institute of Hydrodynamics SB RASNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia
  3. 3.CMAF-CIOUniversity of LisbonLisbonPortugal
  4. 4.Instituto de Matemática InterdisciplinarUniversidad Complutense de MadridSpain

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