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

A singularly perturbed boundary value problem for a second-order ordinary differential equation known in applications as a stationary reaction–diffusion equation is studied. A new class of problems is considered, namely, problems with nonlinearity having discontinuities localized in some domains, wh...

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Bibliographic Details
Published inComputational mathematics and mathematical physics Vol. 55; no. 12; pp. 2001 - 2007
Main Authors Nefedov, N. N., Ni, Minkang
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.12.2015
Springer Nature B.V
Subjects
Approximation
Asymptotic methods
Boundary value problems
Computational mathematics
Computational Mathematics and Numerical Analysis
Differential equations
Mathematical analysis
Mathematics
Mathematics and Statistics
Ordinary differential equations
Partial differential equations
Physics
Studies
internal layers
singular perturbations
asymptotic methods
one-dimensional reaction–diffusion equation
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Summary:A singularly perturbed boundary value problem for a second-order ordinary differential equation known in applications as a stationary reaction–diffusion equation is studied. A new class of problems is considered, namely, problems with nonlinearity having discontinuities localized in some domains, which leads to the formation of sharp transition layers in these domains. The existence of solutions with an internal transition layer is proved, and their asymptotic expansion is constructed.
ISSN:0965-5425
1555-6662
DOI:10.1134/S096554251512012X