caa a22 4500 378847848 CHVBK 20180305123316.0 cr unu---uuuuu 161128e20030601xx s 000 0 eng 10.1515/156939803322380828 doi (NATIONALLICENCE)gruyter-10.1515/156939803322380828 Dymnikov V. P. Institute of Numerical Mathematics of the Russian Academy of Sciences, Moscow GSP-1, 119991, Russia Adjoint equations, integral conservation laws, and conservative difference schemes for nonlinear equations of mathematical physics [Elektronische Daten] [V. P. Dymnikov] In this paper, we consider problems involving the construction of adjoint equations for nonlinear equations of mathematical physics. Hydrodynamical-type systems, in particular, dynamic equations for two-dimensional incompressible ideal fluid are taken as the main subject of investigation. It is shown that using adjoint equations, not only can we construct the known integrals of motion, but also obtain new integrals that are useful, in particular, for investigating the stability of solutions of the original equations. It is also shown that the nonuniqueness of the construction of adjoint equations for original nonlinear problems can be used to construct the finite-dimensional approximations of the original equations. These approximations have the necessary set of finite-dimensional analogues of integral conservation laws. The algorithm for constructing these schemes is given for a problem of two-dimensional ideal incompressible fluid dynamics. Copyright 2003, Walter de Gruyter Russian Journal of Numerical Analysis and Mathematical Modelling Walter de Gruyter 18/3(2003-06-01), 229-242 0927-6467 18:3<229 2003 18 rnam https://doi.org/10.1515/156939803322380828 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/156939803322380828 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Dymnikov V. P. Institute of Numerical Mathematics of the Russian Academy of Sciences, Moscow GSP-1, 119991, Russia NATIONALLICENCE 773 0- Russian Journal of Numerical Analysis and Mathematical Modelling Walter de Gruyter 18/3(2003-06-01), 229-242 0927-6467 18:3<229 2003 18 rnam CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter