The nonlocal bistable equation: Stationary solutions on a bounded interval

Adam J J Chmaj; Xiaofeng Ren

The nonlocal bistable equation: Stationary solutions on a bounded interval

Adam J J Chmaj, Xiaofeng Ren

School of Mathematical & Computer Sciences

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

12 Citations (Scopus)

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 C local minimizers. By taking variations along nonsmooth 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. © 2002 Southwest Texas State University.

Original language	English
Pages (from-to)	XXXXI-XXXXII
Journal	Electronic Journal of Differential Equations
Volume	2002
Publication status	Published - 2002

Keywords

Local minimizers
Monotone solutions

Cite this

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title = "The nonlocal bistable equation: Stationary solutions on a bounded interval",

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 C local minimizers. By taking variations along nonsmooth 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. {\textcopyright} 2002 Southwest Texas State University.",

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year = "2002",

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journal = "Electronic Journal of Differential Equations",

issn = "1072-6691",

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T1 - The nonlocal bistable equation

T2 - Stationary solutions on a bounded interval

AU - Chmaj, Adam J J

AU - Ren, Xiaofeng

PY - 2002

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N2 - 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 C local minimizers. By taking variations along nonsmooth 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. © 2002 Southwest Texas State University.

AB - 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 C local minimizers. By taking variations along nonsmooth 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. © 2002 Southwest Texas State University.

KW - Local minimizers

KW - Monotone solutions

UR - https://www.scopus.com/pages/publications/26244443561

M3 - Article

SN - 1072-6691

VL - 2002

SP - XXXXI-XXXXII

JO - Electronic Journal of Differential Equations

JF - Electronic Journal of Differential Equations

ER -

The nonlocal bistable equation: Stationary solutions on a bounded interval

Abstract

Keywords

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