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Local existence of the solution to the initial-boundary value problem in nonlinear thermomicroelasticity theory

  1. Jerzy Gawinecki*,
  2. Jarosław Łazuka*

Article first published online: 22 DEC 2004

DOI: 10.1002/pamm.200410265

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PAMM

PAMM

Volume 4, Issue 1, pages 568–569, December 2004

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How to Cite

Gawinecki, J. and Łazuka, J. (2004), Local existence of the solution to the initial-boundary value problem in nonlinear thermomicroelasticity theory. Proc. Appl. Math. Mech., 4: 568–569. doi: 10.1002/pamm.200410265

Author Information

  1. Military University of Technology, Institute of Mathematics and Cryptology, Faculty of Cybernetics 00-908 Warsaw, S. Kaliskiego 2, Poland

*Phone: +48 22 683 9687, Fax: +48 22 683 7919

Publication History

  1. Issue published online: 22 DEC 2004
  2. Article first published online: 22 DEC 2004

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Abstract

We prove a theorem about local existence (in time) of the solution to the first initial-boundary value problem for a nonlinear system of equation of the thermomicroelasticity theory. At first, we prove existence, uniqueness and regularity of the solution to this problem for the associated linearized system by using the method of semi-group theory. Next, basing on this theorem, we prove an energy estimate for the solution to the linearized system by applying the method of Sobolev space. At the end, using the Banach fixed point theorem, we prove that the solution of our nonlinear problem exists and is unique. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

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