Exponential stability of c0-semigroup via Lyapunov inequality in Banach space

2021/04/03 by Belabbas Madani, Madani, Belabbas, Zohra Bendaoud +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis #Spectral Theory (math.SP) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2104.01424

openalex publication_date 2021/04/03 · openalex created_date 2021/04/13 · openalex updated_date 2026/07/28

Abstract

We give a relation between the exponential stability of C₀- semigroup T=\lbrace T(t) \rbrace_{t≥ 0} and the solutions of Lyapunov inequality \( ⟨ QAx,x⟨ +⟨ Qx,Ax⟨ ≤ -||x||², \) in B⁺(X,X^*) , with X is a Banach space. The solutions of this inequality characterizes, the boundedness of the resolvent R(λ,A) inside and outside of the left half-plane \Reλ≥ 0 , and also the left invertibility of the C₀- semigroup T.

Related

• On asymptotics for C₀-semigroups
• Uniform bounds of families of analytic semigroups and Lyapunov linear stability of planar fronts
• Refined decay rates of C₀-semigroups on Banach spaces
• Stability criteria for positive semigroups on ordered Banach spaces
• Stability criteria for positive semigroups on ordered Banach spaces