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7.6 Guide to the Literature
de Jager, E.M. and Jiang Furu (1996), The Theory of Singular Perturbations, Elsevier, North-Holland Series in Applied Mathematics and Mechanics 42, Amsterdam.
Dorr, F.W., Parter, S.V., and Shampine, L.F. (1973), Application of the maximum principle to singular perturbation problems, SIAM Rev. 15, pp. 43–88.
Eckhaus, W. (1979), Asymptotic Analysis of Singular Perturbations, North-Holland, Amsterdam. Chapter 7
Eckhaus, W. and de Jager, E.M. (1966), Asymptotic solutions of singular perturbation problems for linear differential equations of elliptic type, Arch. Rat. Mech. Anal. 23, pp. 26–86.
Grasman, J. (1971), On the Birth of Boundary Layers, Mathematical Centre Tract 36, Amsterdam.
Grasman, J. (1974), An elliptic singular perturbation problem with almost characteristic boundaries, J. Math. Anal. Appl. 46, pp. 438–446.
Grasman, J. and van Herwaarden, O.A. (1999), Asymptotic Methods for the Fokker-Planck Equation and the Exit Problem in Applications, Springer-Verlag, New York.
Huet, D. (1977), Perturbations singulières de problèmes elliptiqes, in Lecture Notes in Mathematics 594 (Brauner, C.M., Gay, B., and Mathieu, J., eds.), Springer-Verlag, Berlin.
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Levinson, N. (1950), The first boundary value problem for εΔu+A(x, y)ux+B(x, y)uy+C(x, y)u=D(x, y) for small ε, Ann. Math. 51, pp. 428–445.
Lions, J.L. (1973), Perturbations singulières dans les Problèmes aux Limites et en Contrôle Optimal, Lecture Notes in Mathematics 323, Springer-Verlag, Berlin.
Sanchez Hubert, J. and Sanchez Palencia, E. (1989), Vibration and Coupling of Continuous Systems: Asymptotic Methods, Springer-Verlag, New York.
Trenogin, V.A. (1970), Development and applications of the asymptotic method of Liusternik and Vishik, Usp. Mat. Nauk 25, pp. 123–156; transl. in Russ. Math. Surv. 25, pp. 119–156.
Van Harten, A. (1978), Nonlinear singular perturbation problems: proofs of correctness of a formal approximation based on a contraction principle in a Banach space, J. Math. Anal. Appl. 65, pp. 126–168.
Vishik, M.I. and Liusternik, L.A. (1957), On elliptic equations containing small parameters in the terms with higher derivatives, Dokl. Akad. Nauk, SSR, 113, pp. 734–737.
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(2005). Elliptic Boundary Value Problems. In: Methods and Applications of Singular Perturbations. Texts in Applied Mathematics, vol 50. Springer, New York, NY. https://doi.org/10.1007/0-387-28313-7_7
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