Optimal Control Problem for Fourth-Order Bianchi Equation in Variable Exponent Sobolev Spaces-Reference-Cited by-同舟云学术

Optimal Control Problem for Fourth-Order Bianchi Equation in Variable Exponent Sobolev Spaces

Published:2024-06-30 Issue:1 Volume:16 Page:45-63
ISSN:2148-1830
Container-title:Turkish Journal of Mathematics and Computer Science
language:
Short-container-title:

Author:

Özen Kemal¹^ORCID

Affiliation:

1. NAMIK KEMAL ÜNİVERSİTESİ

Abstract

This work proposes a necessary and sufficient condition such as Pontryagin’s maximum principle for an optimal control problem with distributed parameters, which is described by the fourth-order Bianchi equation involving coefficients in variable exponent Lebesgue spaces. The problem is studied by aid of a novel version of the increment method that essentially uses the concept of the adjoint equation of integral type.

Publisher

Turkish Journal of Mathematics and Computer Science, Association of Mathematicians

Reference32 articles.

1. Akhiev, S.S., The general form of linear bounded functionals in an anisotropic space of S. L. Sobolev type, Doklady Akademii Nauk Azerbaijan SSR, 35(6)(1979), 3–7 (in Russian).

2. Akhiev, S.S., Fundamental solutions of some local and nonlocal boundary value problems and their representations, Doklady Akademii Nauk SSSR, 271(2)(1983), 265–269 (in Russian).

3. Akhmedov, K.T., Akhiev, S.S., Necessary conditions for optimality for some problems in optimal control theory, Doklady Akademii Nauk Azerbaijan SSR, 28(5) (1972), 12–16 (in Russian).

4. Aramaki, J., An extension of a variational inequality in the Simader theorem to a variable exponent Sobolev space and applications: the Dirichlet case, International Journal of Analysis and Applications, 20(2022), Article number 13.

5. Bandaliyev, R.A., Guliyev, V.S., Mamedov, I.G., Rustamov, Y.I., Optimal control problem for Bianchi equation in variable exponent Sobolev spaces, Journal of Optimization Theory and Applications, 180(1)(2019), 303–320.