Институт вычислительной математики
и математической геофизики

The International Conference on Computational Mathematics


Invited papers

Adjoint equations, integral conservation laws, and conservative difference schemes for nonlinear equations of mathematical physics

Dymnikov V.P.

Institute of Numerical Mathematics RAS (Moscow)

In this paper, we consider problems involving the construction of adjoint equations for nonlinear equations of mathematical phisics. Hydrodynamical-tipe 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.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 withthe necessary set of finite-dimensional analoges of integral conservation lows.

Note. Abstracts are published in author's edition

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