Partial differential equations V :
Partial differential equations V : asymptotic methods for partial differential equations /
M.V. Fedoryuk
- Berlin : Springer, 1999
- 247 pages ; 24 cm
- Encyclopaedia of mathematical sciences ; 34 .
Equations with Rapidly Oscillating Solutions -- Asymptotic Expansion as t → ∞ of the Solutions of Exterior Boundary Value Problems for Hyperbolic Equations and Quasiclassical Approximations -- The Higher-Dimensional WKB Method or Ray Method. Its Analogues and Generalizations -- Semiclassical Asymptotics of Eigenfunctions -- The Boundary Layer
The second stage is to determine these functions and coefficients using a direct substitution of the ansatz in the equation, the boundary conditions and the initial conditions. Sometimes it is necessary to use different ansiitze in different domains, and in the overlapping parts of these domains the formal asymptotic solutions must be asymptotically equivalent (the method of matched asymptotic expansions). The basis for success in the search for formal asymptotic solutions is a suitable choice of ansiitze. The study of the asymptotics of explicit solutions of special model problems allows us to "surmise" what the correct ansiitze are for the general solution.
9783540533719
Ecuaciones en derivadas parciales
Differential equations, Partial
Ecuaciones diferenciales
Differential equations
515.353
Equations with Rapidly Oscillating Solutions -- Asymptotic Expansion as t → ∞ of the Solutions of Exterior Boundary Value Problems for Hyperbolic Equations and Quasiclassical Approximations -- The Higher-Dimensional WKB Method or Ray Method. Its Analogues and Generalizations -- Semiclassical Asymptotics of Eigenfunctions -- The Boundary Layer
The second stage is to determine these functions and coefficients using a direct substitution of the ansatz in the equation, the boundary conditions and the initial conditions. Sometimes it is necessary to use different ansiitze in different domains, and in the overlapping parts of these domains the formal asymptotic solutions must be asymptotically equivalent (the method of matched asymptotic expansions). The basis for success in the search for formal asymptotic solutions is a suitable choice of ansiitze. The study of the asymptotics of explicit solutions of special model problems allows us to "surmise" what the correct ansiitze are for the general solution.
9783540533719
Ecuaciones en derivadas parciales
Differential equations, Partial
Ecuaciones diferenciales
Differential equations
515.353