Category: Slow motion and metastability for a nonlocal evolution equation

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The aim of this paper is to contribute to the definition of a versatile language for metastability in the context of partial differential equations of evolutive type. Sign in Help View Cart. Article Tools. Add to my favorites. Recommend to Library. Email to a friend. Digg This.

Notify Me! E-mail Alerts. RSS Feeds. SIAM J. Related Databases. Web of Science You must be logged in with an active subscription to view this. Keywords metastabilityslow motionspectral analysisviscous conservation laws. Publication Data. Publisher: Society for Industrial and Applied Mathematics. Corrado Mascia and Marta Strani. Cited by On the speed rate of convergence of solutions to conservation laws with nonlinear diffusions.

Nonlinear Analysis Journal of Evolution Equations 20 :2, European Journal of Applied Mathematics 31 :1, Complex Variables and Elliptic Equations 1 Advances in Nonlinear Analysis 7 :1, Journal of Hyperbolic Differential Equations 14 Asymptotic Analysis 98 Nonlinearity 28 Journal of Dynamics and Differential Equations 27 :1, Banner art adapted from a figure by Hinke M.In this paper we consider a nonlocal evolution equation in one dimension, which describes the dynamics of a ferromagnetic system in the mean field approximation.

In the presence of a small magnetic field, it admits two stationary and homogeneous solutions, representing the stable and metastable phases of the physical system. We prove the existence of an invariant, one dimensional manifold connecting the stable and metastable phases. This is the unstable manifold of a distinguished, spatially nonhomogeneous, stationary solution, called the critical droplet.

We also obtain a new proof of the existence of the critical droplet, which is supplied with a local uniqueness result. This is a preview of subscription content, log in to check access. Rent this article via DeepDyve. Bates, P. Fife, X. Ren, and X.

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Wang, Traveling waves in a convolution model for phase transitions, Arch. Rational Mech. Google Scholar. Chen, Existence, uniqueness and asymptotic stability of traveling waves in nonlocal evolution equations, Adv.

Differential Equations 2 Chmaj and X. Ren, Homoclinic solutions of an integral equation: existence and stability, J. Differential Equation Carr and R.

Edinburgh Sect. A Pure Appl. Cassandro, A. Galves, E. Olivieri, and E. Vares, Metastable behavior of stochastic dynamics: A pathwise approach, J. De Masi, T. Gobron, and E. Presutti, Traveling fronts in non-local evolution equations, Arch. De Masi, E. Presutti, Spectral properties of integral operators in problems of interface dynamics and metastability, Markov Process.In this paper we consider a non local evolution equation in one dimension, which describes the dynamics of a ferromagnetic system in the mean eld approximation.

In the presence of a small external magnetic eld, this equation admits two stationary homogeneous solutions, which represent the stable and metastable phases of the physical system. We prove the existence of an invariant, one dimensional manifold connecting the stable and metastable phases.

Tunneling in Two Dimensions

This is the unstable manifold of a distinguished, spatially non homogeneous, stationary solution of the evolution equation, called the critical droplet. We show that the points on the manifold are droplets longer or shorter than the critical one, and that their motion is very slow in agreement with the theory of metastable patterns. The existence of the critical droplet was rstly proved in [7], but no uniqueness result was guaranteed by that approach.

However we give here a dierent proof, which is also supplied with a local uniqueness result. Finally, a detailed description of the spatial structure of the critical droplet is given, which will be also a key tool to study the global structure of the unstable manifold. Documents: Advanced Search Include Citations. Abstract In this paper we consider a non local evolution equation in one dimension, which describes the dynamics of a ferromagnetic system in the mean eld approximation.

Powered by:.In this paper we consider a non local evolution equation in one dimension, which describes the dynamics of a ferromagnetic system in the mean eld approximation. In the presence of a small external magnetic eld, this equation admits two stationary homogeneous solutions, which represent the stable and metastable phases of the physical system. We prove the existence of an invariant, one dimensional manifold connecting the stable and metastable phases.

This is the unstable manifold of a distinguished, spatially non homogeneous, stationary solution of the evolution equation, called the critical droplet. We show that the points on the manifold are droplets longer or shorter than the critical one, and that their motion is very slow in agreement with the theory of metastable patterns. The existence of the critical droplet was rstly proved in [7], but no uniqueness result was guaranteed by that approach.

However we give here a dierent proof, which is also supplied with a local uniqueness result. Finally, a detailed description of the spatial structure of the critical droplet is given, which will be also a key tool to study the global structure of the unstable manifold. Provided by: CiteSeerX. Suggested articles.Tunneling is studied here as a variational problem formulated in terms of a functional which approximates the rate function for large deviations in Ising systems with Glauber dynamics and Kac potentials, [9].

The spatial domain is a two-dimensional square of side L with reflecting boundary conditions. For L large enough the penalty for tunneling from the minus to the plus equilibrium states is determined. Minimizing sequences are fully characterized and shown to have approximately a planar symmetry at all times, thus departing from the Wulff shape in the initial and final stages of the tunneling. In a final section Sect. This is a preview of subscription content, log in to check access.

Rent this article via DeepDyve. Alberti G. Bellettini G. Bodineau T. Chen X.

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Google Scholar. Chmaj A. Comets F.

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Cassandro M. De Masi A. Markov Process. Related Fields 4, 27— Related Fields 6, — Nonlinearity 7, 1— Edinburgh Sect.They often think too highly of themselves and have little respect for others.

SIAM Journal on Mathematical Analysis

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slow motion and metastability for a nonlocal evolution equation

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slow motion and metastability for a nonlocal evolution equation

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Slow Motion and Metastability for a Nonlocal Evolution Equation

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