Clustering layers and boundary layers in spatially inhomogeneous phase transition problems

Kimie Nakashima; Kazunaga Tanaka

Annales de l'I.H.P. Analyse non linéaire (2003)

  • Volume: 20, Issue: 1, page 107-143
  • ISSN: 0294-1449

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Nakashima, Kimie, and Tanaka, Kazunaga. "Clustering layers and boundary layers in spatially inhomogeneous phase transition problems." Annales de l'I.H.P. Analyse non linéaire 20.1 (2003): 107-143. <http://eudml.org/doc/78569>.

@article{Nakashima2003,
author = {Nakashima, Kimie, Tanaka, Kazunaga},
journal = {Annales de l'I.H.P. Analyse non linéaire},
language = {eng},
number = {1},
pages = {107-143},
publisher = {Elsevier},
title = {Clustering layers and boundary layers in spatially inhomogeneous phase transition problems},
url = {http://eudml.org/doc/78569},
volume = {20},
year = {2003},
}

TY - JOUR
AU - Nakashima, Kimie
AU - Tanaka, Kazunaga
TI - Clustering layers and boundary layers in spatially inhomogeneous phase transition problems
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2003
PB - Elsevier
VL - 20
IS - 1
SP - 107
EP - 143
LA - eng
UR - http://eudml.org/doc/78569
ER -

References

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  1. [1] S. Ai, S.P. Hastings, A shooting approach to layers and chaos in a forced duffing equation, I, Preprint. Zbl1025.34015MR1935609
  2. [2] Ambrosetti A., Badiale M., Cingolani S., Semiclassical states of nonlinear Schrödinger equations, Arch. Rat. Mech. Anal.140 (1997) 285-300. Zbl0896.35042MR1486895
  3. [3] Angenent S.B., Mallet-Paret J., Peletier L.A., Stable transition layers in a semilinear boundary value problem, J. Differential Equations67 (1987) 212-242. Zbl0634.35041MR879694
  4. [4] Chen C.-N., Multiple solutions for a class of nonlinear Sturm–Liouville problems on the half line, J. Differential Equations85 (1990) 236-275. Zbl0703.34032MR1054550
  5. [5] del Pino M., Felmer P., Local mountain passes for semilinear elliptic problems in unbounded domains, Calc. Var. PDE4 (1996) 121-137. Zbl0844.35032MR1379196
  6. [6] del Pino M., Felmer P., Multi-peak bound states of nonlinear Schrödinger equations, Ann. IHP, Analyse Nonlinéaire15 (1998) 127-149. Zbl0901.35023MR1614646
  7. [7] Fleor A., Weinstein A., Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential, J. Funct. Anal.69 (3) (1986) 397-408. Zbl0613.35076MR867665
  8. [8] Gedeon T., Kokubu H., Mischaikow K., Oka H., Chaotic solutions in slowly varying perturbations of Hamiltonian systems with applications to shallow water sloshing, J. Dynam. Differential Equations14 (2002) 63-84. Zbl1005.37028MR1878245
  9. [9] Gui C., Existence of multi-bump solutions for nonlinear Schrödinger equations via variational method, Comm. Partial Differential Equations21 (1996) 787-820. Zbl0857.35116MR1391524
  10. [10] Gui C., Wei J., Multiple interior peak solutions for some singularly perturbed Neumann problems, J. Differential Equations158 (1999) 1-27. Zbl1061.35502MR1721719
  11. [11] Hemple J.A., Multiple solutions for a class of nonlinear boundary value problems, Indiana Univ. Math. J.20 (11) (1971) 983-996. Zbl0225.35045MR279423
  12. [12] Kang X., Wei J., On interacting bumps of semi-classical states of nonlinear Schrödinger equations, Adv. Differential Equations5 (2000) 899-928. Zbl1217.35065MR1776345
  13. [13] Kath W.L., Slowly varying phase planes and boundary-layer theory, Stud. Appl. Math.72 (3) (1985) 221-239. Zbl0586.76047MR790130
  14. [14] Li Y.-Y., On a singularly perturbed elliptic equation, Adv. Differential Equations2 (1997) 955-980. Zbl1023.35500MR1606351
  15. [15] K. Nakashima, Multi-layered stationary solutions for a spatially inhomogeneous Allen–Cahn equation, J. Differential Equations, to appear. Zbl1034.34024MR1973289
  16. [16] Nakashima K., Stable transition layers in a balanced bistable equation, Differential Integral Equations13 (2000) 1025-1038. Zbl0981.34011MR1775244
  17. [17] Oh Y.-G., Existence of semiclassical bound states of nonlinear Schrödinger equations with potentials of the class (V)a, Comm. Partial Differential Equations13 (1988) 1499-1519. Zbl0702.35228MR970154
  18. [18] Oh Y.-G., Stability of semiclassical bound states of nonlinear Schrödinger equations with potentials, Comm. Math. Phys.121 (1989) 11-33. Zbl0693.35132MR985612
  19. [19] Oh Y.-G., On positive multi-lump bound states of nonlinear Schrödinger equations under multiple well potential, Comm. Math. Phys.131 (1990) 223-253. Zbl0753.35097MR1065671
  20. [20] Rabinowitz P.H., On a class of nonlinear Schrödinger equations, Z. Angew. Math. Phys.43 (1992) 270-291. Zbl0763.35087MR1162728
  21. [21] Wang X., On concentration of positive bound states of nonlinear Schrödinger equations, Comm. Math. Phys.153 (1993) 229-244. Zbl0795.35118MR1218300

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