Stationary layered solutions in R2 for an Allen-Cahn system with multiple well potential

Calculus of Variations and Partial Differential Equations

Volumn 5, Issue 4, 1997, Pages 359-390

  Alama, Stanley ^a   Bronsard, Lia ^a   Gui, Changfeng ^b  

^a MCMASTER UNIVERSITY   (Canada)

^b UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0010533179     PISSN: 09442669     EISSN: None     Source Type: Journal    
DOI: 10.1007/s005260050071     Document Type: Article

References (18)

1. S. Alama, Y. Y. Li, On "multibump" bound states for certain semilinear elliptic equations, Indiana U. Math. Jour., 41 (1993), 983-1026
2. P. Bates, X. Ren, Transition layer solutions of a high order equation in an infinite tube, Comm. PDE, to appear
3. 2 for a Variational Problem with a Symmetric Three Well Potential, Comm. Pure Appl. Math., 49, (1996), 677-715
4. L. Bronsard, F. Reitich, On three-phase boundary motion and the singular limit of a vector-valued Ginzburg-Landau equation. Arch. Rat. Mech. Anal., 124 (1993), 355-379
5. L. Caffarelli, N. Garofalo, F. Segala, A Gradient Bound for Entire Solutions of Quasi-Linear Equations and Its Consequences, Comm. Pure Appld. Math., 47 (1994), 1457-1473
6. V. Coti-Zelati, P. Rabinowitz, Homoclinic orbits for second order Hamiltonian systems possessing superquadratic potentials. Jour. A.M.S., 4 (1992), 693-727
7. E. De Giorgi, Convergence problems for functionals and operators, pp. 131-188, in: Proc. Int. Meeting on Recent Methods in Nonlinear Analysis, Rome, 1978. E. de Giorgi, E. Magenes, and U. Mosco, eds., Pitagora, Bologna, 1979
8. H. Dang, P. Fife, L. Peletier, Saddle solutions of the bistable diffusion equation, Z. Angew Math. Phys., 43 (1992), 984-998
9. p Weights and Unique Continuation, Indiana U. Math. Jour., 35 (1986), 245-267
10. L. Modica, S. Mortola, Some entire solutions in the plane of nonlinear Poisson equations, Boll. Un. Mat. Ital., 5 (1980), 614-622
11. P. Rabinowitz, Heteroclinics for a reversible Hamiltonian system, Ergodic Theory and Dynamical Sys., 14 (1994), 817-829
12. P. Rabinowitz, Heteroclinics for a reversible Hamiltonian system II, Differential and Integral Equqtions, 7 (1994), 1557-1572
13. P. Rabinowitz, Periodic and heteroclinic orbits for a periodic Hamiltonian system, AIHP Analyse non linéaire, 6 (1989), 331-346
14. P. Rabinowitz, A variational approach to heteroclinic orbits for a class of Hamiltonian systems, Frontiers in Pure and Applied Math., R. Dautray, ed. (1991), 267-278
15. P. Rabinowitz, Solutions of heteroclinic type for some classes of semilinear elliptic partial differential equations, J. Math. Sci. Univ. Tokyo, 1 (1994), 525-550
16. J. Rubinstein, P. Sternberg, J. Keller, Fast reaction, slow diffusion, and curve shortening, SIAM Appl. Math., 48 (1989), 1722-1733
17. M. Schatzman, On the stability of the the saddle solution of Allen-Cahn equation, Proc. Royal Soc. Edinburgh, 125 A (1995), 1241-1275
18. P. Sternberg, Vector-valued local minimizers of nonconvex variational problems, Rocky Mt. J. Math, 21 (2) (1991), 799-807