The Nonlocal Bistable Equation: Stationary Solutions on a Bounded Interval

Date

2002-01-02

Authors

Chmaj, Adam J. J.
Ren, Xiaofeng

Journal Title

Journal ISSN

Volume Title

Publisher

Southwest Texas State University, Department of Mathematics

Abstract

We discuss instability and existence issues for the nonlocal bistable equation. This model arises as the Euler-Lagrange equation of a nonlocal, van der Waals type functional. Taking the viewpoint of the calculus of variations, we prove that for a class of nonlocalities this functional does not admit nonconstant C1 local minimizers. By taking variations along non-smooth paths, we give examples of nonlocalities for which the functional does not admit local minimizers having a finite number of discontinuities. We also construct monotone solutions and give a criterion for nonexistence of nonconstant solutions.

Description

Keywords

Local minimizers, Monotone solutions

Citation

Chmaj, A. J. J., & Ren, X. (2002). The nonlocal bistable equation: Stationary solutions on a bounded interval. <i>Electronic Journal of Differential Equations, 2002</i>(02), pp. 1-12.

Rights

Attribution 4.0 International

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