Abstract
<abstract><p>Previously, boundary control problems for parabolic type equations were considered. A portion of the thin rod boundary has a temperature-controlled heater. Its mode of operation should be found so that the average temperature in some region reaches a certain value. In this article, we consider the boundary control problem for the pseudo-parabolic equation. The value of the solution with the control parameter is given in the boundary of the interval. Control constraints are given such that the average value of the solution in considered domain takes a given value. The auxiliary problem is solved by the method of separation of variables, and the problem under consideration is reduced to the Volterra integral equation. The existence theorem of admissible control is proved by the Laplace transform method.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference26 articles.
1. B. D. Coleman, W. Noll, An Approximation Theorem for Functionals, with Applications in Continuum Mechanics, Arch. Rational Mech. Anal., 6 (1960), 355–370. https://doi.org/10.1007/BF00276168
2. B. D. Coleman, R. J. Duffin, V. J. Mizel, Instability, uniqueness, and nonexistence theorems for the equation on a strip, Arch. Rational Mech. Anal., 19 (1965), 100–116. https://doi.org/10.1007/BF00282277
3. L. W. White, Point control approximations of parabolic problems and pseudo-parabolic problems, Appl. Anal., 12 (1981), 251–263. https://doi.org/10.1080/00036818108839365
4. I. E. Egorov, E. S. Efimova, Boundary value problem for third order equation not presented with respect to the highest derivative, Mat. Zamet., 24 (2017), 28–36. https://doi.org/10.25587/SVFU.2018.4.11314
5. A. I. Kozhanov, The existence of regular solutions of the first boundary value Problem for one class of Sobolev type equations with alternating direction, Mat. Zamet. YaGU, 2 (1997), 39–48.
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献