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GLOBAL SOLUTION TO THE INITIAL VALUE PROBLEM FOR NONLINEAR SYSTEM OF EQUATIONS OF THERMODIFFUSION WITHOUT DISPLACEMENTS

GLOBAL SOLUTION TO THE INITIAL VALUE PROBLEM FOR NONLINEAR SYSTEM OF EQUATIONS OF THERMODIFFUSION... DEMONSTRATIO MATHEMATICAVol. XXXVIINo 32004Jarosiaw LazukaG L O B A L SOLUTION T O T H E INITIAL V A L U E P R O B L E MF O R N O N L I N E A R S Y S T E M OF EQUATIONS OFTHERMODIFFUSION WITHOUT DISPLACEMENTSAbstract. In the paper we shall present the proof of global-in-time solution to theinitial value problem for nonlinear partial differential equations describing physical proccesses of thermodiffusion without displacements. Time decay of global solution will bealso shown.1. IntroductionThe aim of this paper is to prove the existence and uniqueness of globalin-time solution to the initial value problem for a nonlinear partial differential equation (pde) system describing a special case of thermodiffusion ofsolids in three-dimensional space. In these solids we have the field of temperature 0\ and chemical potential 62 without displacements [8], [9].The equations describing this type of solid have form(1.1)(fcA-cdt)0i =ddt02,(1.2)( D A - ndt) 62 =ddt6\with the initial conditions(1.3)0 i ( O , x ) = 0°(:r),(1.4)e2{<ò,x) = e 0 2{x),whereare temperature and chemical potential respectively, both depending o n t e R + and x 6 R 3 .The system (1.1)—(1.2) is nonlinear because the physical parametersk, http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

GLOBAL SOLUTION TO THE INITIAL VALUE PROBLEM FOR NONLINEAR SYSTEM OF EQUATIONS OF THERMODIFFUSION WITHOUT DISPLACEMENTS

Łazuka, Jarosław
Demonstratio Mathematica , Volume 37 (3): 14 – Jul 1, 2004
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References (10)

Publisher
de Gruyter
Copyright
© by Jarosław Łazuka
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-2004-0307
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATIO MATHEMATICAVol. XXXVIINo 32004Jarosiaw LazukaG L O B A L SOLUTION T O T H E INITIAL V A L U E P R O B L E MF O R N O N L I N E A R S Y S T E M OF EQUATIONS OFTHERMODIFFUSION WITHOUT DISPLACEMENTSAbstract. In the paper we shall present the proof of global-in-time solution to theinitial value problem for nonlinear partial differential equations describing physical proccesses of thermodiffusion without displacements. Time decay of global solution will bealso shown.1. IntroductionThe aim of this paper is to prove the existence and uniqueness of globalin-time solution to the initial value problem for a nonlinear partial differential equation (pde) system describing a special case of thermodiffusion ofsolids in three-dimensional space. In these solids we have the field of temperature 0\ and chemical potential 62 without displacements [8], [9].The equations describing this type of solid have form(1.1)(fcA-cdt)0i =ddt02,(1.2)( D A - ndt) 62 =ddt6\with the initial conditions(1.3)0 i ( O , x ) = 0°(:r),(1.4)e2{<ò,x) = e 0 2{x),whereare temperature and chemical potential respectively, both depending o n t e R + and x 6 R 3 .The system (1.1)—(1.2) is nonlinear because the physical parametersk,

Journal

Demonstratio Mathematica – de Gruyter

Published: Jul 1, 2004

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