Smooth Lyapunov Manifolds and Correct Mathematical Simulation of Nonlinear Singular Problems in Mathematical Physics
Several problems in various fields of mathematical physics occur lead to the systems of ordinary differential equations (ODEs) having singularities or being defined on an infinite interval. For different classes of linear and nonlinear ODEs, there are many publications dealing with correct statement of singular boundary value problems (BVPs) and their reduction to the equivalent regular ones (see, e.g., the reviews1, 2). This paper deals with some results of 3–5 obtained in the indicated direction for autonomous systems (ASs) of nonlinear ODEs and their application to singular BVPs arising from hydrodynamics.
KeywordsArbitrary Real Number Finite Point Infinite Interval Hyperbolic Equilibrium Nonlinear ODEs
Unable to display preview. Download preview PDF.
- 5.N.B. Konyukhova, Soobsch. po Prikl. Mat. VC RAN ( VC RAN, Moscow, 1996 ) (in Russian).Google Scholar
- 6.N.B. Konyukhova., A.I. Sukov, in: The basic physical-mathematical problems and the technical-technological system simulation ( STANKIN, Moscow, 2001 ), 117–121 (in Russian).Google Scholar
- 11.V.N. Diesperov, Soobsch. po Prikl. Mat. VC AN SSSR ( VC AN SSSR, Moscow, 1986 ) (in Russian).Google Scholar
- 12.H. Schlichting, Grenzschicht-Theorie (Karlsruhe, 1951 ).Google Scholar
- 18.L.D. Landau and E.M. Lifshits, Theoretical Physics, v.V1: Hydrodynamics ( Nauka, Moscow, 1986 ) (in Russian).Google Scholar