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CONVERGENCE TO EQUILIBRIUM FOR A PARABOLIC–HYPERBOLIC PHASE-FIELD SYSTEM WITH NEUMANN BOUNDARY CONDITIONS

HAO WU

Institute of Mathematics, Fudan University, Shanghai, 200433, P. R. China

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MAURIZIO GRASSELLI

Dipartimento di Matematica "F. Brioschi", Politecnico di Milano, Milano, 20133, Italy

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SONGMU ZHENG

Institute of Mathematics, Fudan University, Shanghai, 200433, P. R. China

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https://doi.org/10.1142/S0218202507001851Cited by:22 (Source: Crossref)

Abstract

This paper is concerned with the asymptotic behavior of global solutions to a parabolic–hyperbolic coupled system which describes the evolution of the relative temperature θ and the order parameter χ in a material subject to phase transitions. For the system with homogeneous Neumann boundary conditions for both ¸ and χ, under the assumption that the nonlinearities λ and ϕ are real analytic functions, we prove the convergence of a global solution to an equilibrium as time goes to infinity by means of a suitable Łojasiewicz–Simon type inequality.

Keywords:

AMSC: 35B40, 80A22

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