Keywords
- Singular Perturbation Problem
- Singular Line
- Conjugate Harmonic Function
- Boundary Layer Correction
- Singular Elliptic Equation
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References
Weinstein, A., Discontinuous integrals and generalized potential theory, Trans. Amer. Math. Soc., 63 (1948), 342–354.
_____, Generalized axially symmetric potential theory, Bull. Amer. Math. Soc., 59 (1953), 20–37.
_____, Singular partial differential equations and their applications, in Fluid Dynamics and Applied Mathematics (Proc. Sympos., U. of Maryland, 1961), pp. 29–49, Gordon and Breach, New York, 1962.
Huber, A., On the uniqueness of generalized axially symmetric potentials, Ann. of Math., (2) 60 (1954), 351–358.
_____, Some results on generalized axially symmetric potentials, Proc. Conf. on Diff. Equn. (dedicated to A. Weinstein), U. of Maryland (1955), 147–155.
Quinn, D. W., and Weinacht, R. J., Boundary value problems in generalized bi-axially symmetric potential theorem, Journal of Diff. Equs. (to appear).
Moss, W. F., Boundary value problems and fundamental solutions for degenerate or singular second order linear elliptic partial differential equations, Ph.D. thesis, U. of Delaware (1974).
Eckhaus, W., and de Jager, E. M., Asymptotic solutions of singular perturbation problems for linear differential equations of elliptic type, Arch. Rational Mech. and Anal., 23 (1966), 26–86.
Knowles, J. K., The Dirichlet problem for a thin rectangle, Pro. Edinburgh Math. Soc., 15 (1967), 315–320.
Lions, J. L., Perturbation Singulières dans les Problèmes aux Limites et en Contrôle Optimal, Lecture Notes in Math., No. 323, Springer-Verlag (1973), pp. 227–238.
Jiji, L. M., Singular-perturbation solutions of conduction in irregular domains, Quart. J. Mech. Appl. Math., 27 (1974), 45–55.
Ho, T. C., and Hsiao, G. C., A singular perturbation arising in catalytic reactions in finite cylindrical supports and some related problems, A. I. Ch. E. J. (to appear).
Levinson, N., The first boundary value problem for ɛΔu+Aux+Buy+Cu=D for small ɛ, Ann. of Math., 51 (1950), 227–238.
Keller, J. B., Perturbation Theory, Lectures Notes, Michigan State Univ., East Lansing, Michigan (1968), pp. 55–59.
Hsiao, G. C., and Weinacht, R. J., On a class of singular partial differential equations with a small parameter (in preparation).
Hopf, E., A remark on linear elliptic differential equations of second order, Proc. Am. Math. Soc., 3 (1952), 791–793.
Muckenhaupt, B., and Stein, E. M., Classical expansions and their relation to conjugate harmonic functions, Trans. Amer. Math. Soc., 118 (1965), 17–92.
Parter, S. V., On the existence and uniqueness of symmetric axially symmetric potentials, Arch. Rational Mech. Anal., 20 (1965), 279–286.
Courant, R., and Hilbert, D., Methods of Mathematical Physics, Vol. II, Interscience (1962), pp. 326–331.
Watson, G. N., A Treatise On the Theory of Bessel Functions, Second Edition, Cambridge Univ. Press, 1944.
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Hsiao, G.C., Weinacht, R.J. (1976). Singular perturbation problems for a class of singular partial differential equations. In: Everitt, W.N., Sleeman, B.D. (eds) Ordinary and Partial Differential Equations. Lecture Notes in Mathematics, vol 564. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087341
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DOI: https://doi.org/10.1007/BFb0087341
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