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Title of Journal: Arch Rational Mech Anal

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Abbravation: Archive for Rational Mechanics and Analysis

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Springer-Verlag

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10.1007/bf03043808

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1432-0673

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The Toda System and Clustering Interfaces in the A

Authors: Manuel Del Pino Michał Kowalczyk Juncheng Wei
Publish Date: 2008/07/29
Volume: 190, Issue: 1, Pages: 141-187
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Abstract

We consider the Allen–Cahn equation varepsilon2Delta u + 1u2u = 0 in a bounded smooth domain Ω in mathbbR2 under zero Neumann boundary conditions where varepsilon 0 is a small parameter Let Γ0 be a segment contained in Ω connecting orthogonally the boundary Under certain nondegeneracy and nonminimality assumptions for Γ0 satisfied for instance by the short axis in an ellipse we construct for any given N ≥ 1 a solution exhibiting N transition layers whose mutual distances are Ovarepsilonlogvarepsilon and which collapse onto Γ0 as varepsilonto 0 Asymptotic location of these interfaces is governed by a Todatype system and yields in the limit broken lines with an angle at a common height and at main order cutting orthogonally the boundary

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Other Papers In This Journal:
  1. Optimal Design in Conductivity Under Locally Constrained Heat Flux
  2. Regularity Issues in the Problem of Fluid Structure Interaction
  3. Negative Eigenvalues of Two-Dimensional Schrödinger Operators
  4. Dobrushin States in the $${\phi^4_1}$$ Model
  5. The Liouville Theorem and the L 2 Decay for the FENE Dumbbell Model of Polymeric Flows
  6. The Liouville Theorem and the L 2 Decay for the FENE Dumbbell Model of Polymeric Flows
  7. Counterexamples to the Sonic Criterion
  8. Dislocation Dynamics: Short-time Existence and Uniqueness of the Solution
  9. On Nonlinear Stochastic Balance Laws
  10. Weak Solutions of the Navier–Stokes Equations for Compressible Flows in a Half-Space with No-Slip Boundary Conditions
  11. Generalized Transition Fronts for One-Dimensional Almost Periodic Fisher-KPP Equations
  12. The Gel’fand Problem for the Biharmonic Operator
  13. The Existence Problem for Steiner Networks in Strictly Convex Domains
  14. Stability of Detonation Profiles in the ZND Limit
  15. Uniqueness of Absolute Minimizers for $${L^\infty}$$-Functionals Involving Hamiltonians $${H(x,p)}$$H(x,p)
  16. A Condition for the Hölder Regularity of Local Minimizers of a Nonlinear Elastic Energy in Two Dimensions
  17. Kinetic Stabilization¶of a Nonlinear Sonic Phase Boundary
  18. A Stability Criterion for Two-Fluid Interfaces and Applications
  19. Long-Time Convergence of an Adaptive Biasing Force Method: The Bi-Channel Case
  20. Displacement Convexity and Minimal Fronts at Phase Boundaries
  21. Gradient Bounds for Elliptic Problems Singular at the Boundary
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