zbMATH — the first resource for mathematics

Singular perturbations of parabolic equations without boundary layers. (English) Zbl 1252.35028
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.
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
Full Text: DOI
[1] DOI: 10.1063/1.2169443 · doi:10.1063/1.2169443
[2] DOI: 10.1215/S0012-7094-46-01331-2 · Zbl 0061.19509 · doi:10.1215/S0012-7094-46-01331-2
[3] DOI: 10.1140/epjd/e2004-00075-5 · doi:10.1140/epjd/e2004-00075-5
[4] Akhmetov DR, Asymptot. Anal. 35 pp 65– (2003)
[5] Akhmetov DR, Diff. Integral Equ. 17 pp 99– (2004)
[6] DOI: 10.1007/s00028-006-0294-3 · Zbl 1130.35009 · doi:10.1007/s00028-006-0294-3
[7] DOI: 10.1016/j.jde.2006.06.011 · Zbl 1107.35054 · doi:10.1016/j.jde.2006.06.011
[8] DOI: 10.3934/cpaa.2007.6.1051 · Zbl 1140.35360 · doi:10.3934/cpaa.2007.6.1051
[9] DOI: 10.1103/RevModPhys.77.137 · doi:10.1103/RevModPhys.77.137
[10] Akhmetov DR, Electron. J. Diff. Equ. 24 pp 1– (2002)
[11] DOI: 10.1023/A:1010423209940 · doi:10.1023/A:1010423209940
[12] DOI: 10.1023/A:1010445414795 · doi:10.1023/A:1010445414795
[13] Lavrentiev MM, Diff. Integral Equ. 13 pp 649– (2000)
[14] DOI: 10.1103/PhysRevLett.81.2229 · doi:10.1103/PhysRevLett.81.2229
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.