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Article information
2004 , Volume 9, ¹ 2, p.92-102
Fedorov V.E., Plekhanova M.V.
Weak solutions and the problem of quadratic regulator for degenerate differential equation in Hilbert space
The concept of weak solutions of the Cauchy problem for linear equation of Sobolev type L x(t)=Mx(t)+y(t) allows to extend the set of admissible initial values of the problem and to relax the conditions on the smoothness of the function y(t). The existence and uniqueness of the weak solution of the Cauchy problem and the solution of the problem on quadratic regulator for this equation are established in the case of strongly (L,p)-radial operator M. The obtained abstract results are applied to the problem of optimal control for a certain class of partial differential equations.
[full text] Classificator Msc2000:- *34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions
- 34G10 Linear equations
- 49K20 Problems involving partial differential equations
Keywords: Sobolev type equations, semigroups of operators, weak solution, optimal control, linear Sobolev-type equation, weak solution, optimal control
Author(s):
Fedorov V.E.
PhD. , Associate Professor
Position: Associate Professor
Address: 454021, Russia, Chelyabinsk
Phone Office: (3512) 42 04 09
E-mail: kar@csu.ru
Plekhanova Marina Vasilyevna
Position: Student
Address: 454046, Russia, Chelyabinsk, Novorossiyskaya Str., 122, 45
E-mail: karina@csu.ac.ru
Bibliography link:
Fedorov V.E., Plekhanova M.V. Weak solutions and the problem of quadratic regulator for degenerate differential equation in Hilbert space // Computational technologies. 2004. V. 9. ¹ 2. P. 92-102
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