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Asymptotic behaviour for a phase field model in higher order Sobolev spaces. (English) Zbl 1009.35011

The phase field model with various boundary conditions is rewritten in an evolution form using corresponding Sobolev spaces. The authors prove that, under suitable growth and sign conditions on the nonlinear term, the solutions are globally defined. Then the asymptotic behavior of solutions is analyzed.

MSC:

35B40 Asymptotic behavior of solutions to PDEs
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35B35 Stability in context of PDEs
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