Results 141 to 150 of about 12,187,697 (193)

On the Goursat classification problem

Programming and Computer Software, 2012
In the paper, the Goursat problem--classification of nonlinear hyperbolic differential equations possessing two characteristic invariants--is considered. An algorithm for finding the characteristic invariants is described. On the basis of the algorithm implemented in REDUCE, the characteristic invariants of two Laine's equations are verified.
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Explicit controllability criteria for Goursat problems

Optimization, 1989
In this paper necessary and sufficient rank criteria of exact controllability of linear Goursat problems with constant coefficients are derived, which are a generalization of the Kalman criterion well-known from the control theory of linear systems of ordinary differential equations.
J. Bergmann, P. Burgmeir, P. Weiher
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Generalized goursat problem for a nonlinear differential equation

Ukrainian Mathematical Journal, 1984
Translation from Ukr. Mat. Zh. 36, No.1, 110-114 (Russian) (1984; Zbl 0542.35020).
Kovach, Yu. I., Bojtsun, S. A.
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NECESSARY CONDITIONS FOR OPTIMALITY IN ONE NONSMOOTH OPTIMAL CONTROL PROBLEM FOR GOURSAT-DARBOUX SYSTEMS

Advances in Differential Equations and Control Processes
We consider a nonsmooth optimal control problem described by a system of second-order hyperbolic equations with Goursat boundary conditions. A number of necessary optimality conditions are proved in terms of directional derivatives.
A. Ramazanova
semanticscholar   +1 more source

ON MULTIPOINT NECESSARY CONDITIONS FOR OPTIMALITY OF THE FIRST AND SECOND ORDER SINGULARITIES IN ONE BOUNDARY VALUE PROBLEM GOURSAT-DARBOUX SYSTEMS CONTROL

International Conference on Modern Problems of Mathematics, Mechanics and their Applications
. One boundary value problem of optimal control of Goursat-Darboux systems is considered, under the assumption that the control domain is open. An analogue of the Euler equation is proved and necessary conditions for second-order optimality are derived ...
Vusala Suleymanova
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Euler Scheme for a Stochastic Goursat Problem

Stochastic Analysis and Applications, 2004
We show the Euler approximation for the solution of a stochastic Goursat problem converges in the mean-square to its solution and obtain the rate of convergence for the Euler scheme.
Yenkun Huang, Che-Yuan Tsai
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UNIQUENESS CLASSES FOR THE SOLUTION OF GOURSAT'S PROBLEM

Mathematics of the USSR-Izvestiya, 1974
Uniqueness classes for the solution of Goursat's problem, which consists in giving Cauchy initial conditions for each of the variables , , are studied for linear partial differential equations with constant coefficients with two groups of variables: time and space .
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Solution of the Goursat Problem for the Boussinesq–Love Equation with the Bessel Operator by the Method of Transmutation Operators

Lobachevskii Journal of Mathematics, 2023
S. Karimov, Sh. A. Oripov
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The Goursat problem for a third-order pseudo-parabolic equation with the Bessel operator

NOVEL TRENDS IN RHEOLOGY IX, 2023
S. Karimov, Khojiakbar A. Yulbarsov
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Existence of Weak Solutions for a Degenerate Goursat‐Type Linear Problem

Mathematical methods in the applied sciences
For a generalization of the Gellerstedt operator with mixed‐type Dirichlet boundary conditions to a suitable Tricomi domain, we prove the existence and uniqueness of weak solutions of the linear problem and for a generalization of this problem.
Olimpio Hiroshi Miyagaki, Carlos Alberto Reyes Peña, Rodrigo da Silva Rodrigues   +2 more
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