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Asymptotic expansion of double Laplace-type integrals with a curve of minimal points and application to an exit time problem

In: Mathematica Slovaca, vol. 67, no. 3
Abdallah Benaissa - Moussa Benlahcene
Detaily:
Rok, strany: 2017, 737 - 750
Kľúčové slová:
asymptotic expansion, Laplace-type integrals, minimal curve, exit time problem
O článku:
In this paper we consider the problem of the asymptotic expansion of double Laplace-type integrals, in the case when the set $γ$ of points where the phase achieves its absolute minimum is a simple curve. It will be shown that the asymptotic behaviour of such integrals is governed by the order of degeneracy of normal derivatives of the phase with respect to the curve $γ$. Complete asymptotic expansions will be constructed if that order is constant along $γ$, and the first two coefficients will be explicitly computed. If not, a uniform asymptotic expansion method, involving special functions, is suggested.
Ako citovať:
ISO 690:
Benaissa, A., Benlahcene, M. 2017. Asymptotic expansion of double Laplace-type integrals with a curve of minimal points and application to an exit time problem. In Mathematica Slovaca, vol. 67, no.3, pp. 737-750. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0006

APA:
Benaissa, A., Benlahcene, M. (2017). Asymptotic expansion of double Laplace-type integrals with a curve of minimal points and application to an exit time problem. Mathematica Slovaca, 67(3), 737-750. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0006
O vydaní:
Publikované: 27. 6. 2017