Transformation operators in controllability problems for the degenerate wave equation with variable coefficients

• Дата: 2018
• Автори: Fardigola, L. V., Фардигола, Л. В.
• Формат: Стаття
• Мова: Українська
• Опубліковано: Institute of Mathematics, NAS of Ukraine 2018
• Онлайн доступ: https://umj.imath.kiev.ua/index.php/umj/article/view/1623
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

We study the control system $w_{tt} = \cfrac1{\rho } (kw_x) x + \gamma w,\; w(0, t) = u(t),\; x \in (0, l), t \in (0, T)$, in special modified spaces of the Sobolev type. Here, $\rho , k,$ and \gamma are given functions on $[0, l)$; $u \in L^{\infty} (0, T)$ is a control, and $T > 0$ is a...