Previous article Singular Perturbations in the First Boundary Value Problem for Parabolic EquationsCharles J. HollandCharles J. Hollandhttps://doi.org/10.1137/0508027PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractThe first boundary value problem for singularly perturbed semilinear parabolic equations is considered. The regular and ordinary boundary layer expansions are derived using probabilistic methods.[1] D. G. Aronson, Linear parabolic differential equations containing a small parameter, J. Rational Mech. Anal., 5 (1956), 1003–1014 MR0088660 0073.31803 Google Scholar[2] W. Eckhaus and , E. M. de Jager, Asymptotic solutions of singular perturbation problems for linear differential equations of elliptic type, Arch. Rational Mech. Anal., 23 (1966), 26–86 10.1007/BF00281135 MR0206464 0151.15101 CrossrefISIGoogle Scholar[3] Wendell H. Fleming, Stochastically perturbed dynamical systems, Rocky Mountain J. Math., 4 (1974), 407–433 MR0356224 0297.60030 CrossrefGoogle Scholar[4] Charles J. Holland, Singular perturbations in elliptic boundary value problems, J. Differential Equations, 20 (1976), 248–265 10.1016/0022-0396(76)90105-4 MR0481432 0317.35033 CrossrefISIGoogle Scholar Previous article FiguresRelatedReferencesCited ByDetails Multi-dimensional initial-boundary value problems with strong nonlinearitiesArchive for Rational Mechanics and Analysis, Vol. 91, No. 2 | 1 Jun 1986 Cross Ref Uniformly convergent difference method for the convection-diffusion singular perturbation problem in a curved boundary regionApplied Mathematics and Mechanics, Vol. 7, No. 3 | 1 Mar 1986 Cross Ref Probabilistic representations of boundary layer expansionsStochastic Systems: Modeling, Identification and Optimization, I | 23 February 2009 Cross Ref Volume 8, Issue 2| 1977SIAM Journal on Mathematical Analysis179-374 History Submitted:17 January 1975Published online:17 February 2012 InformationCopyright © 1977 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0508027Article page range:pp. 368-374ISSN (print):0036-1410ISSN (online):1095-7154Publisher:Society for Industrial and Applied Mathematics