کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4615461 | 1339317 | 2015 | 46 صفحه PDF | دانلود رایگان |

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.
Journal: Journal of Mathematical Analysis and Applications - Volume 423, Issue 1, 1 March 2015, Pages 410–455