Multi-layer solutions for an elliptic problem.

DOI10.1016/S0022-0396(03)00176-1zbMath1109.35042MaRDI QIDQ1414011

Shusen Yan, E. Norman Dancer

Publication date: 19 November 2003

Published in: Journal of Differential Equations (Search for Journal in Brave)

zbMATH Keywords

singular perturbationvariational methodsNeumann problemreduction methodelliptic problemmulti-layerinternal layer

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Singular perturbations in context of PDEs (35B25) Nonlinear elliptic equations (35J60)

Related Items (17)

Boundary layer and spike layer solutions for a bistable elliptic problem with generalized boundary conditions ⋮ Morse index of layered solutions to the heterogeneous Allen-Cahn equation ⋮ Phase transition layers for Fife-Greenlee problem on smooth bounded domain ⋮ Interface foliation near minimal submanifolds in Riemannian manifolds with positive Ricci curvature ⋮ Clustering of boundary interfaces for an inhomogeneous Allen-Cahn equation on a smooth bounded domain ⋮ Connectivity of boundaries by clustering phase transition layers of Fife-Greenlee problem on smooth bounded domain ⋮ Locations of interior transition layers to inhomogeneous transition problems in higher -dimensional domains ⋮ Interface foliation for an inhomogeneous Allen-Cahn equation in Riemannian manifolds ⋮ Transition layer for the heterogeneous Allen-Cahn equation ⋮ Positive clustered layered solutions for the Gierer-Meinhardt system ⋮ Phase transition layers with boundary intersection for an inhomogeneous Allen-Cahn equation ⋮ The heterogeneous Allen-Cahn equation in a ball: Solutions with layers and spikes ⋮ Multiple stable patterns in a balanced bistable equation with heterogeneous environments ⋮ Multiple clustered layer solutions for semilinear Neumann problems on a ball ⋮ Stable transition layers in an unbalanced bistable equation ⋮ Solutions with transition layer and spike in an inhomogeneous phase transition model ⋮ On a phase field problem driven by interface area and interface curvature

Cites Work

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• Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential
• A shooting approach to layers and chaos in a forced Duffing equation
• Multi-layered stationary solutions for a spatially inhomogeneous Allen--Cahn equation.
• Layers and spikes in non-homogeneous bistable reaction-diffusion equations
• Boundary concentration phenomena for a singularly perturbed elliptic problem

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