Stability of the interface in a model of phase separation

The paper is concerned with the asymptotic behaviour of the solutions to a nonlocal evolution equation which arises in models of phase separation. As in the Allen–Cahn equations, stationary spatially nonhomogeneous solutions exist, which represent the interface profile between stable phases. Local stability of these interface profiles is proved.

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Asymptotic behaviour of a nonautonomous evolution equation governed by a quasi-nonexpansive operator

Optimization ◽

10.1080/02331934.2021.1949314 ◽

2021 ◽

pp. 1-33

Author(s):

Ming Zhu ◽

Rong Hu ◽

Ya-Ping Fang

Keyword(s):

Evolution Equation ◽

Asymptotic Behaviour ◽

Nonexpansive Operator

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Asymptotic behaviour of solutions to non-isothermal phase separation model with constraint in one-dimensional space

Journal of the Mathematical Society of Japan ◽

10.2969/jmsj/05020491 ◽

1998 ◽

Vol 50 (2) ◽

pp. 491-519 ◽

Cited By ~ 1

Author(s):

Akio ITO ◽

Nobuyuki KENMOCHI

Keyword(s):

Phase Separation ◽

Asymptotic Behaviour ◽

Dimensional Space ◽

One Dimensional ◽

Asymptotic Behaviour Of Solutions ◽

Separation Model

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The optimal interface profile for a non-local model of phase separation*

Nonlinearity ◽

10.1088/0951-7715/15/5/314 ◽

2002 ◽

Vol 15 (5) ◽

pp. 1621-1651 ◽

Cited By ~ 3

Author(s):

Marzio Cassandro ◽

Enza Orlandi ◽

Pierre Picco

Keyword(s):

Phase Separation ◽

Local Model ◽

Non Local ◽

Interface Profile

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On a nonlinear and nonlocal evolution equation related to muscle contraction

Nonlinear Analysis ◽

10.1016/0362-546x(89)90003-5 ◽

1989 ◽

Vol 13 (10) ◽

pp. 1149-1162 ◽

Cited By ~ 5

Author(s):

Pierluigi Colli

Keyword(s):

Evolution Equation ◽

Muscle Contraction ◽

Nonlocal Evolution Equation

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Decay estimates in the supremum norm for the solutions to a nonlinear evolution equation

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210512001163 ◽

2014 ◽

Vol 144 (3) ◽

pp. 557-566 ◽

Cited By ~ 8

Author(s):

Petri Juutinen

Keyword(s):

Evolution Equation ◽

Asymptotic Behaviour ◽

Decay Rate ◽

Nonlinear Evolution Equation ◽

Nonlinear Evolution ◽

Supremum Norm ◽

Decay Estimates ◽

Lateral Boundary ◽

Boundary Values ◽

Image Position

We study the asymptotic behaviour, as t → ∞, of the solutions to the nonlinear evolution equationwhere ΔpNu = Δu + (p−2) (D2u(Du/∣Du∣)) · (Du/∣Du∣) is the normalized p-Laplace equation and p ≥ 2. We show that if u(x,t) is a viscosity solution to the above equation in a cylinder Ω × (0, ∞) with time-independent lateral boundary values, then it converges to the unique stationary solution h as t → ∞. Moreover, we provide an estimate for the decay rate of maxx∈Ω∣u(x,t) − h(x)∣.

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