The Nonlocal Bistable Equation: Stationary Solutions on a Bounded Interval
| dc.contributor.author | Chmaj, Adam J. J. | |
| dc.contributor.author | Ren, Xiaofeng | |
| dc.date.accessioned | 2020-07-07T19:25:16Z | |
| dc.date.available | 2020-07-07T19:25:16Z | |
| dc.date.issued | 2002-01-02 | |
| dc.description.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. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 12 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.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. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/11980 | |
| dc.language.iso | en | |
| dc.publisher | Southwest Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2002, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
| dc.subject | Local minimizers | |
| dc.subject | Monotone solutions | |
| dc.title | The Nonlocal Bistable Equation: Stationary Solutions on a Bounded Interval | |
| dc.type | Article |