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Zeitschrift für Analysis und ihre Anwendungen


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Volume 19, Issue 1, 2000, pp. 121–130
DOI: 10.4171/ZAA/942

Published online: 2000-03-31

Initial-Boundary Value Problem for Some Coupled Nonlinear Parabolic System of Partial Differential Equations Appearing in Thermodiffusion in Solid Body

Jerzy A. Gawinecki[1], P. Kacprzyk[2] and B. Bar-Joseph[3]

(1) Military University of Technology, Warszawa, Poland
(2) Military University of Technology, Warszawa, Poland
(3) Technion - Israel Institute of Technology, Haifa, Israel

We prove a theorem about existence, uniqueness and regularity of the solution to an initial-boundary value problem for a nonlinear coupled parabolic system consisting of two equations. Such a system appears in the thermodiffusion in solid body. In our proof we use an energy method, methods of Sobolev spaces, semigroup theory and the Banach fixed point theorem.

Keywords: Linear and nonlinear parabolic systems of partial differential equations, initial-boundary value problems, energy estimates, Sobolev spaces, semigroup theory, Banach fixed point theorem

Gawinecki Jerzy, Kacprzyk P., Bar-Joseph B.: Initial-Boundary Value Problem for Some Coupled Nonlinear Parabolic System of Partial Differential Equations Appearing in Thermodiffusion in Solid Body. Z. Anal. Anwend. 19 (2000), 121-130. doi: 10.4171/ZAA/942