Some Asymptotic Results For Phase Transition Models
نویسنده
چکیده
This thesis analyzes two types of phase transition models, namely the Cahn–Hilliard model and the Becker–Döring model. In the Cahn–Hilliard setting, this thesis establishes a second-order Γ-convergence result for the mass-constrained Cahn–Hilliard energy. This is obtained using a new variant of the Pòlya–Szegő inequality, along with some new regularity results for the isoperimetric function. For the Becker– Döring model, decay rates towards equilibrium are proved for certain broad classes of subcritical data. This is obtained by using new linear stability estimates and semigroup extension results, along with some classical interpolation inequalities.
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