Zeitschrift für Analysis und ihre Anwendungen
Vol. 19, No. 1, pp. 121-130 (2000)
Initial-Boundary Value Problem for Some Coupled Nonlinear Parabolic System of Partial Differential Equations Appearing in Thermodiffusion in Solid Body
J. Gawinecki, P. Kacprzyk and P. Bar-YosephJ. Gawinecki: Inst. Math. & Oper. Res., Military Univ. Techn. Warsaw, Poland
Inst. 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 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
Classification (MSC2000): 35E15, 35K15, 35K25, 35K50, 35K30
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Electronic fulltext finalized on: 25 Jul 2001. This page was last modified: 9 Nov 2001.