Abstract
We obtain conditions to find the distributed optimal control for parabolic-hyperbolic equations with nonlocal boundary conditions and general quadratic criterion in the special norm. The unique solvability of systems for finding the optimal solution is established, systems’ kernels are estimated, and the convergence of solutions of the problem is proved.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
A. Ashyralyev and A. Yurtsever, “On a nonlocal boundary value problem for semilinear hyperbolic-parabolic equations,” Nonlinear Analysis: Theory, Methods&Applications, 47, No. 5, 3585–3592 (2001).
L. Stupyalis, “A boundary-value problem for the stationary system of equations of magnetohydrodynamics. Boundary-value problems of mathematical physics,” Tr. MIAN SSSR, 147, No. 10, 169–193 (1980).
V. O. Kapustyan and I. O. Pyshnograiev, “The existence and uniqueness conditions for the solution of the parabolic–hyperbolic equation with nonlocal boundary conditions,” Naukovi Visti NTUU KPI, No. 4, 72–86 (2012).
A. I. Egorov, Optimal Control of Linear Systems [in Russian], Naukova Dumka, Kyiv (1988).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Kibernetika i Sistemnyi Analiz, No. 3, May–June, 2015, pp. 132–142.
Rights and permissions
About this article
Cite this article
Kapustyan, V.O., Pyshnograiev, I.O. Distributed Control with the General Quadratic Criterion in a Special Norm for Systems Described by Parabolic–Hyperbolic Equations with Nonlocal Boundary Conditions. Cybern Syst Anal 51, 438–447 (2015). https://doi.org/10.1007/s10559-015-9735-8
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10559-015-9735-8