On a finding the coefficient of one nonlinear wave equation in the mixed problem

• Autorzy: Safarova Zimrud R.

Identyfikatory

DOI

10.24425/acs.2020.133497

• Języki publikacji: EN

Abstrakty

EN

The paper is devoted to the finding of the coefficient of one nonlinear wave equation in the mixed problem. The considered problem is reduced to the optimal control problem with proper functional. Differentiability of functional is proved and the necessary optimality conditions are derived in the form of the variational inequality. Existence of the optimal control is proved.

Słowa kluczowe

EN

hyperbolic equation; nonlinear wave equation; optimal control problem; necessary condition

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2020
• Tom: Vol. 30, No. 2
• Strony: 199--212
• Opis fizyczny: Bibliogr. 12 poz., wzory

Twórcy

autor

Safarova Zimrud R.

• Nakhchivan State University, Nakhchivan, Azerbaijan

Bibliografia

• [1] S. I. Kabanikhin, Inverse and Ill Posed Problems, 457 p., Sibirskoe Nauchnoe Izdatelstvo, Degruyter.com, Novosibirsk 2009.
• [2] J. L. Lions, Control of Singular Distributed Systems, 368 p., Nauka, Moscow 1987.
• [3] A. V. Fursikov, Optimal Control of Distributed Systems. Theory and Applications (in Russian), Nauchnaya Kniga, Novosibirsk 1999.
• [4] S. Y. Serovajsky, Optimization and Differentiation, Vol. 2, Evolutional Systems, 329 p., Kazakh Nat. Univ., Almaty 2009.
• [5] H. F. Guliyev and G. G. Ismayilova, The problem of determining the coefficient at the lowest term in the equation of oscillations, Advanced Mathematical Models & Applications, 3(2) (2018), 128–136.
• [6] H. F. Guliyev and Z. R., Safarova, On a determination of the initial functions from the observed values of the boundary functions for the second-order hyperbolic equation, Advanced Mathematical Models & Applications, 3(3) (2018), 215–222.
• [7] X. Wu, L. Mei, and C. Liu, An analytical expression of solutions to nonlinear wave equations in higher dimensions with Robin boundary conditions, Journal of Mathematical Analysis and Applications, 426(2) (2015), 1164–1173.
• [8] S. Pfaff and S. Ulbrich, Optimal boundary control of nonlinear hyperbolic conservation laws with switched boundary data, SIAM Journal on Control and Optimization, 53(3) (2015), 1250–1277.
• [9] A. Mardani, M. R., Hooshmandasl, M. M., Hosseini, and M. H. Heydari, Moving least squares (MLS) method for the nonlinear hyperbolic telegraph equation with variable coefficients, International Journal of Computational Methods, 14(03) (2017), 1750026. 212 Z. R. SAFAROVA
• [10] J-L. Lions, Some Methods of Solution of the Nonlinear Boundary Problems, 587 p., Nauka, Moscow 1972.
• [11] O. A. Ladijenskaya, Boundary Value Problems of Mathematical Physics,408 p., Nauka, Moscow 1973.
• [12] F. P. Vasil’ev, Methods of Solution of the Extremal Problems, 400 p., Nauka, Moscow 1981.

Uwagi

EN

1. All the results obtained in this work are valid if in equation (1) instead of the nonlinear term |u|u set u3 and take n = 3.

PL

2. Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).