Информационная система "Конференции"

All-Russian Conference "New mathematical models of continuum mechanics: Construction and investigation" devoted to 90-years anniversary of academician L. V. Ovsyannikov

Novosibirsk, April 23-28, 2009

Abstracts

Euler-type integrals and multiintegrals of linear partial differential equations

Ganzha E.I.

Dept. Mathematics and Informatics,
Krasnoyarsk State Pedagogical University (Krasnoyarsk)

We present a general theory of explicit solutions of linear PDEs in the plane, obtainable by the classical Laplace cascade method and its modern generalizations. Multiintegrals are expressions of the form $ I = L_1(x,y)f_1(x) + ... + L_k(x,y)f_k(x)$, where $L_i$ are given linear ordinary differential operators w.r.t. $x$ with coefficients depending on $x$, $y$, and $f_i(x)$ are arbitrary functions of $x$.

Possible rigorous definitions of reducibility of such (multi)integrals are given; we prove that various possible definitions are equivalent. Constructive algorithms for checking irreducibility of a given (multi)integral as well as for its reduction to an irreducible form are given.

Note. Abstracts are published in author's edition

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