منابع مشابه
Generalized Solutions of a Periodic Goursat Problem
Under reasonable assumptions on the data u, v and the function f , we show that the nonlinear periodic Goursat problem ∂u ∂x∂y (x, y) = f(x, y, u(x, y)); u(x, 0) = v(x); u(0, y) = w(y) which cannot be posed in the general theory of distributions, may be studied and solved in a differential algebra of periodic new generalized functions on R2. This algebra contains, in a canonical way, the space ...
متن کاملon the goursat problem for a linear partial differential equation
in this paper, the goursat problem of a general form for a linear partial differential equation is investigated with the help of the riemann function method. some results are given concerning the existence and uniqueness for the solution of the suggested problem.
متن کاملThe Bang-bang Principle for the Goursat-darboux Problem*
In the paper, the bang-bang principle for a control system connected with a system of linear nonautonomous partial differential equations of hyperbolic type (the socalled Goursat-Darboux problem or continuous Fornasini-Marchesini problem) is proved. Some density result is also obtained.
متن کاملStability Analysis of Solutions to an Optimal Control Problem Associated with a Goursat-darboux Problem†
The question of the continuous dependence of solutions to an optimal control problem on data (the so-called stability analysis of solutions or well-posedness) is very important from the point of view of practical applications of theory. Indeed, if the problem is related to a physical phenomenon, its data can be considered only an arbitrarily close approximation to exact values. Consequently, if...
متن کاملSecond harmonic generation: Goursat problem on the semi-strip and explicit solutions
A rigorous and complete solution of the initial-boundary-value (Goursat) problem for second harmonic generation (and its matrix analog) on the semi-strip is given in terms of the Weyl functions. A wide class of the explicit solutions and their Weyl functions is obtained also.
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1967
ISSN: 0386-2194
DOI: 10.3792/pja/1195521523