Transformation Operators and Modified Sobolev Spaces in Controllability Problems on a Half-Axis

• Published in: Журнал математической физики, анализа, геометрии
• Date: 2016
• ISSN: 1812-9471
• Main Author: Fardigola, L.V.
• Format: Article
• Language: English
• Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2016
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/140546
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Transformation Operators and Modified Sobolev Spaces in Controllability Problems on a Half-Axis / L.V. Fardigola // Журнал математической физики, анализа, геометрии. — 2016. — Т. 12, № 1. — С. 17-47. — Бібліогр.: 40 назв. — англ.

In the paper, the control system wₜₜ =1/ρ(kwₓ)ₓ + γw, wₓ(0, t) = u(t), x > 0, t belongs (0, T), is considered in special modified spaces of Sobolev type Here ρ, k, and γ are given functions on [0, +∞); u belongs L∞(0, ∞) is a control; T > 0 is a constant. The growth of distributions from thes...