1. Unbounded solutions for a periodic phase transition model.
- Author
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Byeon, Jaeyoung and Rabinowitz, Paul H.
- Subjects
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MATHEMATICAL bounds , *MATHEMATICAL models , *PHASE transitions , *SET theory , *EXISTENCE theorems , *SHADOWING theorem (Mathematics) - Abstract
In an earlier paper, [1] , the authors treated a family of Allen–Cahn model problems for which 0 and 1 are solutions and further solutions were found that are near 1 on a prescribed set, T + Ω , where T ⊂ Z n , and near 0 on ( Z n ∖ T ) + Ω . Here Ω ⊂ ( 0 , 1 ) n . In this paper, a more general class of potentials is treated for which the pair, { 0 , 1 } , is replaced by Z and the existence of a far richer structure of shadowing solutions, including unbounded ones, is established. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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