Asymptotic solutions to Fuchsian equations in several variables

• Autorzy: Boris Sternin , Victor Shatalov
• Języki publikacji: EN

Abstrakty

EN

The aim of this paper is to construct asymptotic solutions to multidimensional Fuchsian equations near points of their degeneracy. Such construction is based on the theory of resurgent functions of several complex variables worked out by the authors in [1]. This theory allows us to construct explicit resurgent solutions to Fuchsian equations and also to investigate evolution equations (Cauchy problems) with operators of Fuchsian type in their right-hand parts.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1996
• Tom: 33
• Numer: 1
• Strony: 351-363

Daty

wydano

1996

Twórcy

autor

Boris Sternin

• Department of Computational Mathematics and Cybernetics, Moscow State University, 119899 Moscow, Russia

autor

Victor Shatalov

• Department of Computational Mathematics and Cybernetics, Moscow State University, 119899 Moscow, Russia

Bibliografia

• [1] B. Yu. Sternin and V. E. Shatalov, On a notion of resurgent function of several variables, Math. Nachr. 171 (1995), 283-301.
• [2] M. Kashiwara and T. Kawai, Second microlocalization and asymptotic expansions, in: Lecture Notes in Phys. 126, Springer, New York, 1980, 21-76.
• [3] R. Melrose, Analysis on Manifolds with Corners, Lecture Notes, MIT, Cambridge, Mass., 1988.
• [4] B.-W. Schulze, Pseudodifferential Operators on Manifolds with Singularities, North-Holland, Amsterdam, 1991.
• [5] B. Ziemian, Elliptic corner operators in spaces with continuous radial asymptotics. I, J. Differential Equations 101 (1993), 28-57.
• [6] B. Ziemian, Elliptic corner operators in spaces with continuous radial asymptotics. II, in: Partial Differential Equations, Banach Center Publ. 27, Inst. of Math., Polish Acad. Sci., Warszawa, 1992, 555-580.
• [7] B.-W. Schulze, B. Sternin and V. Shatalov, Resurgent analysis in the theory of differential equations with singularities, Math. Nachr. 170 (1994), 1-21.
• [8] H. Komatsu, Laplace transform of hyperfunctions. A new foundation of Heaviside calculus, J. Fac. Sci. Univ. Tokyo IA 34 (1987), 805-820.
• [9] B. Candelpergher, J. C. Nosmas and F. Pham, Approche de la Résurgence, Hermann, 1993.
• [10] B. Yu. Sternin and V. E. Shatalov, Differential Equations on Complex Manifolds, Kluwer Acad. Publ., Dordrecht, 1994.
• [11] B. Yu. Sternin and V. E. Shatalov, On a formula for the asymptotic expansion of an integral in complex analysis, Soviet Math. Dokl. 43 (1991), 624-627.
• [12] B. Yu. Sternin and V. E. Shatalov, Stationary phase method for Laplace-Radon transformation, Mat. Zametki 51 (4) (1992), 116-125 (in Russian).
• [13] B. Yu. Sternin and V. E. Shatalov, On exact asymptotics at infinity of solutions to differential equations, preprint, Max-Planck-Institut für Mathematik, Bonn, 1993.
• [14] M. V. Korovina, B. Yu. Sternin and V. E. Shatalov, Asymptotical expansions 'in the large' of solutions of the complex Cauchy problem with singular initial data, Soviet Math. Dokl. 44 (1991), 674-677.