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Mathematical and physical aspect of the solution of the Cauchy problem for a system of equations describing a nonlocal model of propagation of heat with finite speed
Author(s) -
Gawinecki Jerzy August,
Łazuka Jarosław,
Rafa Józef
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200701053
Subject(s) - cauchy problem , sobolev space , initial value problem , mathematics , mathematical analysis , space (punctuation) , basis (linear algebra) , cauchy distribution , heat equation , computer science , geometry , operating system
In our paper we present a new system of equations describing a nonlocal model of propagation of heat with finite speed in three‐dimensional space. Such a system of equations is described by a system of integral – differential equations. At first using the modiffied Cagniard de Hoop method, we construct the fundamental solution of this system of equations. On the basis of the constructed fundamental solution we obtain the explicite formulate of the solution of the Cauchy problem for this system of equations and applying the method of Sobolev and Biesov spaces, we get L p – L q time decay estimate for the solution of the Cauchy problem. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)