Recent developments in applied mathematics and mechanics: theory, experiment and practice. Devoted to the 80th anniversary of academician N.N.Yanenko

Akademgorodok, Novosibirsk, Russia, June 24 - 29, 2001

Abstracts

Russian participants

Application of the method of special series for representation of solutions of nonlinear partial differential equations

Filimonov M.Y.

Institute of Mathematics and Mechanics UrB RAS (Ekaterinburg)

A method of special series is presented. This method is a constructive approach to representing solutions of nonlinear partial differential equations in the form of series with recurrently calculated coefficients by the powers of certain functions (we shall call these functions a basic functions). This method is developed in the academician A.F.Sidorov scientific school. In the paper the up-to-date situation in this field is presented and the following development of the method is suggested for more wide class of nonlinear equations and initial conditions by using new classes of basic functions.

A new method of constructing solutions of nonlinear partial differential equations by using a known exact solution of the equation and the special series method. A known exact solution is suggested to be a 0th term of the series and, using it, to obtain the basic functions and corresponding series. This method is considered for the nonlinear filtration equation, exact solutions of which are known. In this case it is possible to find the basic functions with functional arbitrariness, to investigate the convergency domain of corresponding series, and to construct new classes of solutions of nonlinear equations which contain an arbitrary function.

The work is supported by RFBR projects 00-01-00370, 00-15-96042 and by the program of interdisciplinary projects between UrB RAS and SB RAS.

Full Text in Russian: PDF (666 kb)
Note. Abstracts are published in author's edition

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