Sidewise Profile Control of 1-D Waves

SARAÇ Y., Zuazua E.

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, cilt.193, sa.1-3, ss.931-949, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 193 Sayı: 1-3
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1007/s10957-021-01986-w
  • Dergi Adı: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, ABI/INFORM, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Computer & Applied Sciences, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.931-949
  • Anahtar Kelimeler: 1-D wave equations, Sidewise profile controllability, Nodal profile control, BV-coefficients, Sidewise observability, Sidewise energy estimates, EXACT BOUNDARY CONTROLLABILITY, NODAL PROFILE, NULL CONTROLLABILITY, HEAT-EQUATION, OBSERVABILITY, NETWORK
  • Atatürk Üniversitesi Adresli: Evet

Özet

We analyze the sidewise controllability for the variable coefficients one-dimensional wave equation. The control is acting on one extreme of the string with the aim that the solution tracks a given path or profile at the other free end. This sidewise profile control problem is also often referred to as nodal profile or tracking control. The problem is reformulated as a dual observability property for the corresponding adjoint system, which is proved by means of sidewise energy propagation arguments in a sufficiently large time, in the class of BV-coefficients. We also present a number of open problems and perspectives for further research.