کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4609536 | 1338517 | 2016 | 25 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: On an application of Tikhonov's fixed point theorem to a nonlocal Cahn–Hilliard type system modeling phase separation On an application of Tikhonov's fixed point theorem to a nonlocal Cahn–Hilliard type system modeling phase separation](/preview/png/4609536.png)
This paper investigates a nonlocal version of a model for phase separation on an atomic lattice that was introduced by P. Podio-Guidugli (2006) [36]. The model consists of an initial–boundary value problem for a nonlinearly coupled system of two partial differential equations governing the evolution of an order parameter ρ and the chemical potential μ. Singular contributions to the local free energy in the form of logarithmic or double-obstacle potentials are admitted. In contrast to the local model, which was studied by P. Podio-Guidugli and the present authors in a series of recent publications, in the nonlocal case the equation governing the evolution of the order parameter contains in place of the Laplacian a nonlocal expression that originates from nonlocal contributions to the free energy and accounts for possible long-range interactions between the atoms. It is shown that just as in the local case the model equations are well posed, where the technique of proving existence is entirely different: it is based on an application of Tikhonov's fixed point theorem in a rather unusual separable and reflexive Banach space.
Journal: Journal of Differential Equations - Volume 260, Issue 11, 5 June 2016, Pages 7940–7964