Global solution to the initial value problem for nonlinear system of equations of thermodiffusion without displacements

• Autorzy: Łazuka J.
• Języki publikacji: EN

Abstrakty

EN

In the paper we shall present the proof of global-in-time solution to the initial value problem for nonlinear partial differential equations describing physical proc-cesses of thermodiffusion without displacements. Time decay of global solution will be also shown.

Słowa kluczowe

EN

thermodiffusion; global solutions; local solutions; linear parabolic systems

PL

termodyfuzja; rozwiązania globalne; rozwiązania lokalne; linearne paraboliczne systemy

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2004
• Tom: Vol. 37, nr 3
• Strony: 557--570
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Łazuka J.

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

Bibliografia

• [1] R. A. Adams, Sobolev Spaces, Academic Press, New York, 1975.
• [2] J. Gawinecki, Global solution to the Cauchy problem in non-linear hyperbolic thermoelasticity, Math. Method Appl. Sci. 15 (1992), 223-237.
• [3] F. John, S. Klainerman, Almost global existence to nonlinear wave equations in three space dimensions, Comm. Pure Appl. Math. 37 (1984), 443-455.
• [4] S. Kawashimii, Systems of a hyperbolic-parabolic composite type, with applications to the equations of magnetohydrodynamics, Thesis, Kyoto University, 1983.
• [5] S. Klainerman, Global existence for nonlinear wave equations, Comm. Pure Appl. Math. 33 (1980), 43-101.
• [6] J. Łazuka, A. Szymaniec, Matrix of fundamental solutions for the coupled parabolic system of partial differential equations, Biuletyn WAT, Math, and Oper. Res. 49 (2000), 19-31.
• [7] A. Majda, Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables, Appl. Math. Sci. 53, Springer, New York, 1984.
• [8] W. Nowacki, Dynamical problem of thermodiffusion in solids I, Bull. Acad. Polon. Sci. Ser. Sci. Tech. 22 (1974), 43 [55],
• [9] W. Nowacki, Dynamical problem of thermodiffusion in solids II, Bull. Acad. Polon. Sci. Ser. Sci. Tech. 22 (1974), 129-135.
• [10] R. Racke, Lectures on Nonlinear Evolution Equations, Springer-Verlag, Berlin 1992.
• [11] H. Triebel, Theory of Function Spaces, Monographs Math. 78, Birkhäuser, Besel, 1983.