Singular perturbations of parabolic equations without boundary layers. (English) Zbl 1252.35028

Akhmetov, Denis R.; Lavrentiev, Mikhail M.; Spigler, Renato

Appl. Anal. 90, No. 11-12, 1803-1818 (2011).

In this survey paper, the authors present several classes of singularly perturbed parabolic PDEs. Attention is focused on examples where boundary layers are not needed in order to describe the asymptotic behavior of solutions. This phenomenon is due to the regularity of solutions which may have smooth variations while their gradient may vary rapidly in some subdomains. The article reports results achieved mainly by the authors in the recent years.

Reviewer: Daniel Ševčovič (Bratislava)

MSC:

35B25	Singular perturbations in context of PDEs
35K20	Initial-boundary value problems for second-order parabolic equations
35K70	Ultraparabolic equations, pseudoparabolic equations, etc.
35Q84	Fokker-Planck equations

Keywords:

ultraparabolic equations; survey paper

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