Unbounded solutions for a periodic phase transition model

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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 + Omega, where T subset of Z(n), and near 0 on (Z(n)\T) + Omega. Here Omega subset of (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. (C) 2015 Elsevier Inc. All rights reserved
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2016-01
Language
English
Article Type
Article
Keywords

STATIONARY LAYERED SOLUTIONS; ALLEN-CAHN EQUATIONS; VARIATIONAL-PROBLEMS; ELLIPTIC PROBLEMS; R-N; MULTIPLICITY; R-2; MINIMIZERS; SYSTEMS; TORUS

Citation

JOURNAL OF DIFFERENTIAL EQUATIONS, v.260, no.2, pp.1126 - 1153

ISSN
0022-0396
DOI
10.1016/j.jde.2015.09.024
URI
http://hdl.handle.net/10203/209063
Appears in Collection
MA-Journal Papers(저널논문)
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