Internal layers in the one-dimensional reaction-diffusion equation with a discontinuous reactive term

DOI10.1134/S096554251512012XzbMath1367.34082MaRDI QIDQ266093

Ming Kang Ni, Nikolai N. Nefedov

Publication date: 13 April 2016

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

singular perturbationsasymptotic methodsinternal layersone-dimensional reaction-diffusion equation

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Discontinuous ordinary differential equations (34A36) Singular perturbations for ordinary differential equations (34E15) Asymptotic expansions of solutions to ordinary differential equations (34E05)

Related Items (20)

Existence of contrast structures in a problem with discontinuous reaction and advection ⋮ Time-independent reaction-diffusion equation with a discontinuous reactive term ⋮ Asymptotics of the solution of a singularly perturbed second-order delay differential equation ⋮ A class of singularly perturbed equations with discontinuous right-hand side in the critical case ⋮ Nonsmooth regular perturbations of singularly perturbed problems ⋮ Internal layer for a system of singularly perturbed equations with discontinuous right-hand side ⋮ Multizonal boundary and internal layers in the singularly perturbed problems for a stationary equation of reaction-advection-diffusion type with weak and discontinuous nonlinearity ⋮ On unstable contrast structures in one-dimensional reaction-diffusion-advection problems with discontinuous sources ⋮ Asymptotics of the solution to a stationary piecewise-smooth reaction-diffusion-advection equation ⋮ Internal layers for a singularly perturbed second-order quasilinear differential equation with discontinuous right-hand side ⋮ Internal layer for a singularly perturbed equation with discontinuous right-hand side ⋮ Contrast structures in problems for a stationary equation of reaction-diffusion-advection type with discontinuous nonlinearity ⋮ Use of very weak approximate boundary layer solutions to spatially nonsmooth singularly perturbed problems ⋮ Multizonal internal layers in the singularly perturbed equation with a discontinuous right-hand side ⋮ Solution of contrast structure type for a reaction-diffusion equation with discontinuous reactive term ⋮ Asymptotics of the solution to a stationary piecewise-smooth reaction-diffusion equation with a multiple root of the degenerate equation ⋮ Asymptotic stability of a stationary solution of a multidimensional reaction-diffusion equation with a discontinuous source ⋮ Existence and stability of periodic solution of contrast structure type in discontinuous singularly perturbed reaction-convection-diffusion problem ⋮ Boundary layer solutions to singularly perturbed quasilinear systems ⋮ ON THE ASYMPTOTIC SOLUTION TO A TYPE OF PIECEWISE-CONTINUOUS SECOND-ORDER DIRICHLET PROBLEMS OF TIKHONOV SYSTEM

Cites Work

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• Singularly perturbed problems with boundary and internal layers
• Green's function estimates for a singularly perturbed convection-diffusion problem
• Singularly perturbed boundary value problems in case of exchange of stability
• Asymptotic theory of contrast structures (review)
• Existence and asymptotic stability of periodic solutions with an interior layer of reaction-advection-diffusion equations
• Steplike contrast structure in a singularly perturbed system of equations with different powers of small parameter
• Comparison Principle for Reaction-Diffusion-Advection Problems with Boundary and Internal Layers
• Asymptotic-numerical Investigation of Generation and Motion of Fronts in Phase Transition Models
• The Capriciousness of Numerical Methods for Singular Perturbations
• Numerical Analysis of a 2d Singularly Perturbed Semilinear Reaction-Diffusion Problem

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