کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4609620 1338521 2016 35 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Existence and regularity of solution for a stochastic Cahn–Hilliard/Allen–Cahn equation with unbounded noise diffusion
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Existence and regularity of solution for a stochastic Cahn–Hilliard/Allen–Cahn equation with unbounded noise diffusion
چکیده انگلیسی

The Cahn–Hilliard/Allen–Cahn equation with noise is a simplified mean field model of stochastic microscopic dynamics associated with adsorption and desorption-spin flip mechanisms in the context of surface processes. For such an equation we consider a multiplicative space-time white noise with diffusion coefficient of linear growth. Applying techniques from semigroup theory, we prove local existence and uniqueness in dimensions d=1,2,3d=1,2,3. Moreover, when the diffusion coefficient satisfies a sub-linear growth condition of order α   bounded by 13, which is the inverse of the polynomial order of the nonlinearity used, we prove for d=1d=1 global existence of solution. Path regularity of stochastic solution, depending on that of the initial condition, is obtained a.s. up to the explosion time. The path regularity is identical to that proved for the stochastic Cahn–Hilliard equation in the case of bounded noise diffusion. Our results are also valid for the stochastic Cahn–Hilliard equation with unbounded noise diffusion, for which previous results were established only in the framework of a bounded diffusion coefficient.As expected from the theory of parabolic operators in the sense of Petrovskıı̆, the bi-Laplacian operator seems to be dominant in the combined model.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 260, Issue 3, 5 February 2016, Pages 2383–2417
نویسندگان
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