Гіперболічні системи у просторах Гельфанда і Шилова
Abstract
UDC 517.956.32, 517.955.2 For systems hyperbolic in Shilov's sense with time-dependent coefficients, the properties of the Green function are studied in the $S$-type spaces. For systems of this kind in the indicated spaces, we establish the correct solvability of the Cauchy problem. It is shown that, for each $\beta>1,$ the space ${S_0^\beta}'$ of Gelfand and Shilov distributions is the class of well-posedness of this problem.
Fields of Study & Subjects
Differential Equations and Boundary Problems
Mathematical and Theoretical Analysis
Nonlinear Differential Equations Analysis
Publication details
- Journal / source
- Ukrains’kyi Matematychnyi Zhurnal
- Volume
- 71
- Issue
- 10
- Pages
- 1360–1373
- Publication date
- 9 February 2026
- Language
- EN