Approximate controllability of semilinear deterministic and stochastic evolution equations in abstract spaces

Mahmudov N.

SIAM Journal on Control and Optimization, vol.42, no.5, pp.1604-1622, 2003 (SCI-Expanded, Scopus) identifier

  • Nəşrin Növü: Article / Article
  • Cild: 42 Say: 5
  • Nəşr tarixi: 2003
  • Doi nömrəsi: 10.1137/s0363012901391688
  • jurnalın adı: SIAM Journal on Control and Optimization
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Səhifə sayı: pp.1604-1622
  • Açar sözlər: Controllability, Semilinear evolution equations, Stochastic evolution equations, Symmetric operators, The contraction mapping principle, The schauder fixed point theorem
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Yox

Qısa məlumat

Various sufficient conditions for approximate controllability of linear evolution systems in abstract spaces have been obtained, but approximate controllability of semilinear control systems usually requires some complicated and limited assumptions. In this paper, we show the approximate controllability of the abstract semilinear deterministic and stochastic control systems under the natural assumption that the associated linear control system is approximately control-lable. The results are obtained using new properties of symmetric operators (which are proved in this paper), compact semigroups, the Schauder fixed point theorem, and/or the contraction mapping principle.