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Laplace Invariants for Some Classes of Linear Partial Differential Equations

Laplace Invariants for Some Classes of Linear Partial Differential Equations Differential Equations, Vol. 40, No. 1, 2004, pp. 63–74. Translated from Differentsial'nye Uravneniya, Vol. 40, No. 1, 2004, pp. 58–68. Original Russian Text Copyright c 2004 by Dzhokhadze. PARTIAL DIFFERENTIAL EQUATIONS Laplace Invariants for Some Classes of Linear Partial Di erential Equations O. M. Dzhokhadze Razmadze Mathematical Institute, Academy of Sciences of Georgia, Tbilisi, Georgia Received May 20, 2002 In the present paper, we consider some classes of second- and higher-order linear partial di er- ential equations. We study some of their structural properties on the plane and in space. In par- ticular, we write out Laplace invariants in closed form in all cases and discuss their independence in some sense as well as factorizations of hyperbolic operators and the representability of elliptic and parabolic operators in a form close to the canonical form. 1. LAPLACE INVARIANTS OF SECOND-ORDER EQUATIONS 1 .On the (x;y)-plane, we consider second-order linear partial di erential equations of the general form A(x;y)u + B(x;y)u + C (x;y)u + D(x;y)u + E(x;y)u + F (x;y)u + G(x;y)= 0; (1:1) xx xy yy x y where A, B, C , D, E, F,and G are given real functions and u is the unknown real function. In http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Laplace Invariants for Some Classes of Linear Partial Differential Equations

Dzhokhadze, O.
Differential Equations , Volume 40 (1) – Oct 18, 2004
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References (5)

Publisher
Springer Journals
Copyright
Copyright © 2004 by MAIK “Nauka/Interperiodica”
Subject
Mathematics; Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1023/B:DIEQ.0000028714.62481.2d
Publisher site
See Article on Publisher Site

Abstract

Differential Equations, Vol. 40, No. 1, 2004, pp. 63–74. Translated from Differentsial'nye Uravneniya, Vol. 40, No. 1, 2004, pp. 58–68. Original Russian Text Copyright c 2004 by Dzhokhadze. PARTIAL DIFFERENTIAL EQUATIONS Laplace Invariants for Some Classes of Linear Partial Di erential Equations O. M. Dzhokhadze Razmadze Mathematical Institute, Academy of Sciences of Georgia, Tbilisi, Georgia Received May 20, 2002 In the present paper, we consider some classes of second- and higher-order linear partial di er- ential equations. We study some of their structural properties on the plane and in space. In par- ticular, we write out Laplace invariants in closed form in all cases and discuss their independence in some sense as well as factorizations of hyperbolic operators and the representability of elliptic and parabolic operators in a form close to the canonical form. 1. LAPLACE INVARIANTS OF SECOND-ORDER EQUATIONS 1 .On the (x;y)-plane, we consider second-order linear partial di erential equations of the general form A(x;y)u + B(x;y)u + C (x;y)u + D(x;y)u + E(x;y)u + F (x;y)u + G(x;y)= 0; (1:1) xx xy yy x y where A, B, C , D, E, F,and G are given real functions and u is the unknown real function. In

Journal

Differential Equations – Springer Journals

Published: Oct 18, 2004

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