کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8898673 | 1631494 | 2018 | 48 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Metastability of the Cahn-Hilliard equation in one space dimension
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله

چکیده انگلیسی
We establish metastability of the one-dimensional Cahn-Hilliard equation for initial data that is order-one in energy and order-one in HËâ1 away from a point on the so-called slow manifold with N well-separated layers. Specifically, we show that, for such initial data on a system of lengthscale Î, there are three phases of evolution: (1) the solution is drawn after a time of order Î2 into an algebraically small neighborhood of the N-layer branch of the slow manifold, (2) the solution is drawn after a time of order Î3 into an exponentially small neighborhood of the N-layer branch of the slow manifold, (3) the solution is trapped for an exponentially long time exponentially close to the N-layer branch of the slow manifold. The timescale in phase (3) is obtained with the sharp constant in the exponential.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 265, Issue 4, 15 August 2018, Pages 1528-1575
Journal: Journal of Differential Equations - Volume 265, Issue 4, 15 August 2018, Pages 1528-1575
نویسندگان
Sebastian Scholtes, Maria G. Westdickenberg,