On an Inverse Problem for a One-Dimensional Two-Velocity Dynamical System
- Авторлар: Pestov A.1
-
Мекемелер:
- St.Petersburg Department of the Steklov Mathematical Institute
- Шығарылым: Том 214, № 3 (2016)
- Беттер: 344-371
- Бөлім: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/237395
- DOI: https://doi.org/10.1007/s10958-016-2782-5
- ID: 237395
Дәйексөз келтіру
Аннотация
The evolution of the dynamical system under consideration is governed by the wave equation ρutt − (γux)x + Aux + Bu = 0, x>0, t > 0, with the zero initial Cauchy data and Dirichlet boundary control at x = 0. Here, ρ, γ, A, B are smooth 2 × 2–matrix-valued functions of x; ρ = diag {ρ1, ρ2} and γ = diag {γ1, γ2} are matrices with positive entries; u = u(x, t) is a solution (an ℝ2-valued function). In applications, the system corresponds to one-dimensional models, in which there are two types of wave modes, which propagate with different velocities and interact with each other. The “input→state” correspondence is realized by the response operator R : u(0, t) _→ γ(0)ux(0, t), t ≥ 0, which plays the role of inverse data. The representations for the coefficients A and B, which are used for their determination via the response operator, are derived. An example of two systems with the same response operator is given, where in the first system the wave modes do not interact, whereas in the second one the interaction does occur. Bibliography: 3 titles.
Негізгі сөздер
Авторлар туралы
A. Pestov
St.Petersburg Department of the Steklov Mathematical Institute
Хат алмасуға жауапты Автор.
Email: pestov@pdmi.ras.ru
Ресей, St.Petersburg