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

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

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 languageEnglish
Pages (from-to)707-731
Number of pages25
JournalJournal of Dynamics and Differential Equations
Volume28
Issue number3-4
DOIs
Publication statusPublished - 1 Sep 2016

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