Hypersingular nonlinear boundary-value problems with a small parameter

Andrei D. Polyanin*, Inna K. Shingareva

*Autor correspondiente de este trabajo

Producción científica: Contribución a una revistaArtículorevisión exhaustiva

1 Cita (Scopus)

Resumen

Some hypersingular nonlinear boundary-value problems with a small parameter ε at the highest derivative are described. These problems essentially (qualitatively and quantitatively) differ from the usual linear and quasilinear singularly perturbed boundary-value problems and have the following unusual properties: (i) in hypersingular boundary-value problems, super thin boundary layers arise, and the derivative at the boundary layer can have very large values of the order of e1∕ε and more (in standard problems with boundary layers, the derivative at the boundary has the order of ε−1 or less); (ii) in hypersingular boundary-value problems, the position of the boundary layer is determined by the values of the unknown function at the boundaries (in standard problems with boundary layers, the position of the boundary layer is determined by coefficients of the given equation, and the values of the unknown function at the boundaries do not play a role here); (iii) hypersingular boundary-value problems do not admit a direct application of the method of matched asymptotic expansions (without a preliminary nonlinear point transformation of the equation under consideration). Examples of hypersingular nonlinear boundary-value problems with ODEs and PDEs are given and their exact solutions are obtained.

Idioma originalInglés
Páginas (desde-hasta)93-98
Número de páginas6
PublicaciónApplied Mathematics Letters
Volumen81
DOI
EstadoPublicada - jul. 2018

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© 2018 Elsevier Ltd

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