Stable equilibria of a singularly perturbed reaction–diffusion equation when the roots of the degenerate equation contact or intersect along a non-smooth hypersurface

Arnaldo Simal do Nascimento; Maicon Sônego

doi:10.1007/s00028-015-0304-4

Stable equilibria of a singularly perturbed reaction–diffusion equation when the roots of the degenerate equation contact or intersect along a non-smooth hypersurface

Journal of Evolution Equations ◽

10.1007/s00028-015-0304-4 ◽

2015 ◽

Vol 16 (2) ◽

pp. 317-339

Author(s):

Arnaldo Simal do Nascimento ◽

Maicon Sônego

Keyword(s):

Diffusion Equation ◽

Reaction Diffusion ◽

Singularly Perturbed ◽

Reaction Diffusion Equation ◽

Degenerate Equation ◽

Smooth Hypersurface ◽

Stable Equilibria

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Stable equilibria to a singularly perturbed reaction–diffusion equation in a degenerated heterogeneous environment

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2015.08.071 ◽

2016 ◽

Vol 433 (2) ◽

pp. 1743-1756

Author(s):

Arnaldo Simal do Nascimento ◽

Maicon Sônego

Keyword(s):

Diffusion Equation ◽

Reaction Diffusion ◽

Singularly Perturbed ◽

Reaction Diffusion Equation ◽

Heterogeneous Environment ◽

Stable Equilibria

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The Existence of a Boundary-Layer Stationary Solution to a Reaction–Diffusion Equation with Singularly Perturbed Neumann Boundary Condition

Moscow University Physics Bulletin ◽

10.3103/s0027134920050185 ◽

2020 ◽

Vol 75 (5) ◽

pp. 409-414

Author(s):

N. N. Nefedov ◽

N. N. Deryugina

Keyword(s):

Boundary Layer ◽

Boundary Condition ◽

Diffusion Equation ◽

Stationary Solution ◽

Neumann Boundary Condition ◽

Neumann Boundary ◽

Reaction Diffusion ◽

Singularly Perturbed ◽

Reaction Diffusion Equation

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Layered stable equilibria of a reaction–diffusion equation with nonlinear Neumann boundary condition

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2008.06.001 ◽

2008 ◽

Vol 347 (1) ◽

pp. 123-135 ◽

Cited By ~ 3

Author(s):

Arnaldo Simal do Nascimento ◽

Renato José de Moura

Keyword(s):

Boundary Condition ◽

Diffusion Equation ◽

Neumann Boundary Condition ◽

Neumann Boundary ◽

Reaction Diffusion ◽

Reaction Diffusion Equation ◽

Stable Equilibria

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A Richardson scheme of the decomposition method for solving singularly perturbed parabolic reaction-diffusion equation

Computational Mathematics and Mathematical Physics ◽

10.1134/s0965542510120043 ◽

2010 ◽

Vol 50 (12) ◽

pp. 2003-2022 ◽

Cited By ~ 6

Author(s):

G. I. Shishkin ◽

L. P. Shishkina

Keyword(s):

Diffusion Equation ◽

Decomposition Method ◽

Reaction Diffusion ◽

Singularly Perturbed ◽

Reaction Diffusion Equation

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Improved difference scheme of the solution decomposition method for a singularly perturbed reaction-diffusion equation

Proceedings of the Steklov Institute of Mathematics ◽

10.1134/s0081543811020155 ◽

2011 ◽

Vol 272 (S1) ◽

pp. 197-214 ◽

Cited By ~ 1

Author(s):

G. I. Shishkin ◽

L. P. Shishkina

Keyword(s):

Diffusion Equation ◽

Difference Scheme ◽

Decomposition Method ◽

Reaction Diffusion ◽

Singularly Perturbed ◽

Reaction Diffusion Equation

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Finite difference schemes for the singularly perturbed reaction-diffusion equation in the case of spherical symmetry

Computational Mathematics and Mathematical Physics ◽

10.1134/s0965542509050078 ◽

2009 ◽

Vol 49 (5) ◽

pp. 810-826

Author(s):

G. I. Shishkin ◽

L. P. Shishkina

Keyword(s):

Finite Difference ◽

Diffusion Equation ◽

Spherical Symmetry ◽

Reaction Diffusion ◽

Difference Schemes ◽

Singularly Perturbed ◽

Reaction Diffusion Equation ◽

Finite Difference Schemes

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Difference scheme of the solution decomposition method for a singularly perturbed parabolic reaction–diffusion equation

Russian Journal of Numerical Analysis and Mathematical Modelling ◽

10.1515/rjnamm.2010.017 ◽

2010 ◽

Vol 25 (3) ◽

Cited By ~ 5

Author(s):

G. I. Shishkin

Keyword(s):

Diffusion Equation ◽

Difference Scheme ◽

Decomposition Method ◽

Reaction Diffusion ◽

Singularly Perturbed ◽

Reaction Diffusion Equation

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A class of singularly perturbed initial boundary problem for reaction diffusion equation

Analysis in Theory and Applications ◽

10.1007/bf02835473 ◽

2003 ◽

Vol 19 (1) ◽

pp. 14-19 ◽

Cited By ~ 1

Author(s):

Xie Feng

Keyword(s):

Diffusion Equation ◽

Boundary Problem ◽

Reaction Diffusion ◽

Initial Boundary ◽

Singularly Perturbed ◽

Reaction Diffusion Equation ◽

Initial Boundary Problem

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Improved approximations of the solution and derivatives to a singularly perturbed reaction-diffusion equation based on the solution decomposition method

Computational Mathematics and Mathematical Physics ◽

10.1134/s0965542511060169 ◽

2011 ◽

Vol 51 (6) ◽

pp. 1020-1049 ◽

Cited By ~ 2

Author(s):

G. I. Shishkin ◽

L. P. Shishkina

Keyword(s):

Diffusion Equation ◽

Decomposition Method ◽

Reaction Diffusion ◽

Singularly Perturbed ◽

Reaction Diffusion Equation

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Generalized solution of a class of singularly perturbed robin problems for nonlinear reaction diffusion equation

Wuhan University Journal of Natural Sciences ◽

10.1007/s11859-014-0992-6 ◽

2014 ◽

Vol 19 (2) ◽

pp. 149-152

Author(s):

Qinkuan Wu ◽

Weigang Wang ◽

Xianfeng Chen ◽

Yonghong Xu ◽

Jiaqi Mo

Keyword(s):

Diffusion Equation ◽

Reaction Diffusion ◽

Generalized Solution ◽

Singularly Perturbed ◽

Reaction Diffusion Equation ◽

Nonlinear Reaction ◽

Nonlinear Reaction Diffusion Equation

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