Convergence of the Allen--Cahn Equation with Neumann Boundary Conditions
نویسندگان
چکیده
منابع مشابه
Convergence of the Allen-cahn Equation with Neumann Boundary Conditions
We study a singular limit problem of the Allen-Cahn equation with Neumann boundary conditions and general initial data of uniformly bounded energy. We prove that the time-parametrized family of limit energy measures is Brakke’s mean curvature flow with a generalized right angle condition on the boundary.
متن کاملErratum to "Convergence of the Allen-Cahn Equation with Neumann Boundary Conditions"
In this note we describe the results obtained by the paper (titled the same) which studies a singular limit problem of the Allen-Cahn equation with Neumann boundary conditions and general initial data of uniformly bounded energy. In it we prove that the time-parametrized family of limit energy measures is Brakke’s mean curvature flow with a generalized right angle condition on the boundary.
متن کاملBoundary Interface for the Allen-cahn Equation
We consider the Allen-Cahn equation ε∆u + u− u = 0 in Ω, ∂u ∂ν = 0 on ∂Ω, where Ω is a smooth and bounded domain in R such that the mean curvature is positive at each boundary point. We show that there exists a sequence εj → 0 such that the Allen-Cahn equation has a solution uεj with an interface which approaches the boundary as j → +∞.
متن کاملGlobal Solution to the Allen-cahn Equation with Singular Potentials and Dynamic Boundary Conditions
We prove well-posedness results for the solution to an initial and boundaryvalue problem for an Allen-Cahn type equation describing the phenomenon of phase transitions for a material contained in a bounded and regular domain. The dynamic boundary conditions for the order parameter have been recently proposed by some physicists to account for interactions with the walls (see [14] and [20]). We s...
متن کاملSome Efficient Numerical Solutions of Allen-Cahn Equation with Non-Periodic Boundary Conditions
Abstract: This paper presents some numerical methods for Allen-Cahn equation using different time stepping and space discretization methods with non-periodic boundary conditions. In space the equation is discretized by Chebyshev spectral method, while in time the exponential time differencing fourth-order Runge-Kutta (ETDRK4) and implicit-explicit scheme is used. For comparison we also use the ...
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ژورنال
عنوان ژورنال: SIAM Journal on Mathematical Analysis
سال: 2015
ISSN: 0036-1410,1095-7154
DOI: 10.1137/140987808