Zeitschrift für Analysis und ihre Anwendungen Vol. 19, No. 1, pp. 121130 (2000) 

InitialBoundary Value Problem for Some Coupled Nonlinear Parabolic System of Partial Differential Equations Appearing in Thermodiffusion in Solid BodyJ. Gawinecki, P. Kacprzyk and P. BarYosephJ. Gawinecki: Inst. Math. & Oper. Res., Military Univ. Techn. Warsaw, PolandInst. Math. & Oper. Res., Military Univ. Techn. Warsaw, Poland Fac. Mech. Eng., Technion, Izrael Inst. Techn., Haifa, Izrael Abstract: We prove a theorem about existence, uniqueness and regularity of the solution to an initialboundary 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, initialboundary value problems, energy estimates, Sobolev spaces, semigroup theory, Banach fixed point theorem Classification (MSC2000): 35E15, 35K15, 35K25, 35K50, 35K30 Full text of the article:
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