On the Large Time Behavior of the Solutions of a Nonlocal Ordinary Differential Equation with Mass Conservation

Danielle Hilhorst; Hiroshi Matano; Thanh Nam Nguyen; Hendrik Weber

doi:10.1007/s10884-015-9465-7

On the Large Time Behavior of the Solutions of a Nonlocal Ordinary Differential Equation with Mass Conservation

Danielle Hilhorst, Hiroshi Matano, Thanh Nam Nguyen, Hendrik Weber

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

6 Citations (SciVal)

Abstract

We consider an initial value problem for a nonlocal differential equation with a bistable nonlinearity in several space dimensions. The equation is an ordinary differential equation with respect to the time variable t, while the nonlocal term is expressed in terms of spatial integration. We discuss the large time behavior of solutions and prove, among other things, the convergence to steady-states. The proof that the solution orbits are relatively compact is based upon the rearrangement theory.

Original language	English
Pages (from-to)	707-731
Number of pages	25
Journal	Journal of Dynamics and Differential Equations
Volume	28
Issue number	3-4
DOIs	https://doi.org/10.1007/s10884-015-9465-7
Publication status	Published - 1 Sept 2016

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https://doi.org/10.1007/s10884-015-9465-7

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title = "On the Large Time Behavior of the Solutions of a Nonlocal Ordinary Differential Equation with Mass Conservation",

abstract = "We consider an initial value problem for a nonlocal differential equation with a bistable nonlinearity in several space dimensions. The equation is an ordinary differential equation with respect to the time variable t, while the nonlocal term is expressed in terms of spatial integration. We discuss the large time behavior of solutions and prove, among other things, the convergence to steady-states. The proof that the solution orbits are relatively compact is based upon the rearrangement theory.",

author = "Danielle Hilhorst and Hiroshi Matano and Nguyen, {Thanh Nam} and Hendrik Weber",

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AU - Hilhorst, Danielle

AU - Matano, Hiroshi

AU - Nguyen, Thanh Nam

AU - Weber, Hendrik

PY - 2016/9/1

Y1 - 2016/9/1

N2 - We consider an initial value problem for a nonlocal differential equation with a bistable nonlinearity in several space dimensions. The equation is an ordinary differential equation with respect to the time variable t, while the nonlocal term is expressed in terms of spatial integration. We discuss the large time behavior of solutions and prove, among other things, the convergence to steady-states. The proof that the solution orbits are relatively compact is based upon the rearrangement theory.

AB - We consider an initial value problem for a nonlocal differential equation with a bistable nonlinearity in several space dimensions. The equation is an ordinary differential equation with respect to the time variable t, while the nonlocal term is expressed in terms of spatial integration. We discuss the large time behavior of solutions and prove, among other things, the convergence to steady-states. The proof that the solution orbits are relatively compact is based upon the rearrangement theory.

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JO - Journal of Dynamics and Differential Equations

JF - Journal of Dynamics and Differential Equations

IS - 3-4

ER -

On the Large Time Behavior of the Solutions of a Nonlocal Ordinary Differential Equation with Mass Conservation

Abstract

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