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Название: Representation of solutions of boundary value problems for nonlinear evolution equations by special series with recurrently calculated coefficients
Авторы: Filimonov, M. Yu.
Дата публикации: 2019
Издатель: Institute of Physics Publishing
Библиографическое описание: Filimonov M. Yu. Representation of solutions of boundary value problems for nonlinear evolution equations by special series with recurrently calculated coefficients / M. Yu. Filimonov. — DOI 10.1088/1742-6596/1268/1/012071 // Journal of Physics: Conference Series. — 2019. — Vol. 1. — Iss. 1268. — 12071.
Аннотация: One of the analytical methods of presenting solutions of nonlinear partial differential equations is the method of special series in powers of specially selected functions called basic functions. The coefficients of such series are found successively as solutions of linear differential equations. The basic functions can also contain arbitrary functions. By using such functional arbitrariness allows in some cases, to prove the global convergence of the corresponding constructed series, and also allows us to prove the solvability of the boundary value problem for the Korteweg-de Vries equation. In the paper for a nonlinear wave equation a theorem on the possibility of satisfying a given boundary condition using an arbitrary function contained in the basic function is proved. © Published under licence by IOP Publishing Ltd.
Ключевые слова: BOUNDARY CONDITIONS
BOUNDARY VALUE PROBLEMS
CONTINUUM MECHANICS
KORTEWEG-DE VRIES EQUATION
ANALYTICAL METHOD
ARBITRARY FUNCTIONS
BASIC FUNCTIONS
GLOBAL CONVER-GENCE
LINEAR DIFFERENTIAL EQUATION
NONLINEAR EVOLUTION EQUATION
NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS
NONLINEAR WAVE EQUATION
NONLINEAR EQUATIONS
URI: http://elar.urfu.ru/handle/10995/92597
Условия доступа: info:eu-repo/semantics/openAccess
Идентификатор SCOPUS: 85073910833
Идентификатор WOS: 000561766800071
Идентификатор PURE: 11112511
ISSN: 1742-6588
DOI: 10.1088/1742-6596/1268/1/012071
Сведения о поддержке: Russian Foundation for Basic Research, RFBR: 19–07–00435
The work was supported by Russian Foundation for Basic Research 19–07–00435.
Располагается в коллекциях:Научные публикации, проиндексированные в SCOPUS и WoS CC

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