کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4615461 1339317 2015 46 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On systems of Cahn–Hilliard and Allen–Cahn equations considered as gradient flows in Hilbert spaces
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
On systems of Cahn–Hilliard and Allen–Cahn equations considered as gradient flows in Hilbert spaces
چکیده انگلیسی

We study systems of Allen–Cahn and Cahn–Hilliard equations with the mobility coefficients depending on c and ∇c. We interpret these systems of equations as gradient flows in Hilbert spaces with a densely defined Riemannian metric. In particular, we study gradient flows (curves of maximal slope) of the form∂tu+∇l,uS(u)∋f∂tu+∇l,uS(u)∋f where SS is a nonconvex functional, ∇l,uS(u)∇l,uS(u) is the strong-weak closure of the subgradient of SS and f is a time dependent right hand side. The article generalizes the results by Rossi and Savaré [36] to this setting and applies for systems of multiple phases derived by Heida, Málek and Rajagopal [20] and [19] in a simplified form. More generally, we will show that a certain class of reaction–diffusion equations coming from a modeling approach by Rajagopal and Srinivasa [32] or by Mielke [27], are automatically subject to the presented theory of curves of maximal slope.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 423, Issue 1, 1 March 2015, Pages 410–455
نویسندگان
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