Layers and spikes in non-homogeneous bistable reaction-diffusion equations

DOI10.1090/S0002-9947-06-03834-7zbMath1087.35007OpenAlexW1937519883MaRDI QIDQ3378468

Shangbing Ai, Xinfu Chen, Stuart P. Hastings

Publication date: 3 April 2006

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-06-03834-7

zbMATH Keywords

Morse indexone space dimensionshooting methodhomogeneous Neumann conditionsmultiple layersmultiple spikes

Mathematics Subject Classification ID

Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Nonlinear boundary value problems for ordinary differential equations (34B15) Stability in context of PDEs (35B35) Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57)

Related Items (13)

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 ⋮ Stable transition layer induced by degeneracy of the spatial inhomogeneities in the Allen-Cahn problem ⋮ Persistence and extinction of population in reaction-diffusion-advection model with strong Allee effect growth ⋮ Unusual bifurcation of a Neumann boundary value problem ⋮ Uniform asymptotic expansions of solutions of an inhomogeneous equation ⋮ Multi-layer solutions for an elliptic problem. ⋮ Bifurcation tearing in a forced Duffing equation ⋮ The heterogeneous Allen-Cahn equation in a ball: Solutions with layers and spikes ⋮ Evans functions and bifurcations of nonlinear waves of some nonlinear reaction diffusion equations ⋮ High frequency solutions for the singularly-perturbed one-dimensional nonlinear Schrödinger equation ⋮ On the internal transition layer to some inhomogeneous semilinear problems: interface location ⋮ Patterns Versus Spatial Heterogeneity—From a Variational Viewpoint

Cites Work

• Stable transition layers in a semilinear boundary value problem
• A commentary ``On the periodic solutions of a forced second-order equation by S. P. Hastings and J. B. McLeod
• On the singular problem for the scalar parabolic equation with variable diffusion
• A shooting approach to layers and chaos in a forced Duffing equation
• Multi-bump solutions to Carrier's problem
• Multi-layered stationary solutions for a spatially inhomogeneous Allen--Cahn equation.
• Heteroclinic orbits of semilinear parabolic equations
• Boundary layers in a semilinear parabolic problem
• Existence and stability of transition layers
• Solutions to the Nonautonomous Bistable Equation with Specified Morse Index. Part I: Existence
• Attractors of Some Reaction Diffusion Problems
• Orbit equivalence of global attractors of semilinear parabolic differential equations
• Metastable patterns in solutions of u_t = ϵ²u_xx − f(u)
• Monotone and oscillatory equilibrium solutions of a problem arising in population genetics

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