CONVERGENCE TO EQUILIBRIUM FOR A PARABOLIC–HYPERBOLIC PHASE-FIELD SYSTEM WITH NEUMANN BOUNDARY CONDITIONS
2007 ◽
Vol 17
(01)
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pp. 125-153
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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.
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2012 ◽
Vol 11
(2)
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pp. 547-556
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2020 ◽
Vol 28
(2)
◽
pp. 237-241
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2013 ◽
Vol 265
(3)
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pp. 375-398
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