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Local existence of the solution to the initial-boundary value problem in nonlinear thermodiffusion in micropolar medium. (English) Zbl 0955.35003
Summary: We prove a theorem about local existence (in time) of the solution to the first initial-boundary value problem for a nonlinear hyperbolic-parabolic system of eight coupled partial differential equations of second-order describing the process of thermodiffusion in a three-dimensional micropolar medium. At first, we prove existence, uniqueness and regularity of the solution to this problem for the associated linearized system by using the Faedo-Galerkin method and semigroup theory. Next, we prove (based on this theorem) an energy estimate for the solution to the linearized system by applying the method of Sobolev spaces. Finally, we prove by the Banach fixed point theorem that the solution of our nonlinear problem exists and is unique.

MSC:
35A07 Local existence and uniqueness theorems (PDE) (MSC2000)
74F05 Thermal effects in solid mechanics
47D06 One-parameter semigroups and linear evolution equations
80A20 Heat and mass transfer, heat flow (MSC2010)
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