Abstract
Using probabilistic methods we treat the problem of asymptotic expansions for a class of semilinear elliptic equations depending upon a small parameter ε which degenerate to parabolic equations when ε becomes zero. The method depends upon the representation of the solution of the partial differential equation as the expected value of a functional of an Ito stochastic differential equation.
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References
W. Eckhaus, “Boundary layers in linear elliptic singular perturbation problems”, SIAM Review 14 (1972) 225–270.
W.H. Fleming, “Stochastically perturbed dynamical systems”, Rocky Mountain Journal of Mathematics 4 (1974) 407–433.
C. Holland, “Singular perturbations in elliptic boundary value problems”, Journal Differential Equations 20 (1976) 248–265.
C. Holland, “Parabolic boundary layers”, Indiana University Mathematics Journal, to appear.
C. Holland, “Singular perturbations in the first boundary value problems for parabolic equations”, SIAM Journal of Mathematical Analysis, to appear.
M. Zlamal, “The parabolic equation as a limiting case of a certain elliptic equation”, Annuli di mathematics Pura ed Applicata 52 (1962) 143–150.
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© 1976 The Mathematical Programming Society
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Holland, C.J. (1976). Probabilistic representations of boundary layer expansions. In: Wets, R.J.B. (eds) Stochastic Systems: Modeling, Identification and Optimization, I. Mathematical Programming Studies, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120764
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DOI: https://doi.org/10.1007/BFb0120764
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00783-5
Online ISBN: 978-3-642-00784-2
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