nonlinear semigroup
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2020 ◽  
Vol 26 ◽  
pp. 23
Author(s):  
Mathias Dus ◽  
Francesco Ferrante ◽  
Christophe Prieur

This paper considers a diagonal semilinear system of hyperbolic partial differential equations with positive and constant velocities. The boundary condition is composed of an unstable linear term and a saturated feedback control. Weak solutions with initial data in L2([0, 1]) are considered and well-posedness of the system is proven using nonlinear semigroup techniques. Local L∞ exponential stability is tackled by a Lyapunov analysis and convergence of semigroups. Moreover, an explicit estimation of the region of attraction is given.



2018 ◽  
Vol 38 (6) ◽  
pp. 1637-1654
Author(s):  
Abdul-Majeed AL-IZERI ◽  
Khalid LATRACH


2017 ◽  
Vol 25 (1) ◽  
pp. 43-47 ◽  
Author(s):  
Ahmed H. Soliman ◽  
Dareen N. Ali ◽  
Essam O. Abdel-Rahman


2016 ◽  
Vol 12 (6) ◽  
pp. 6361-6375 ◽  
Author(s):  
Ruijin Lou ◽  
Penghui Lv ◽  
Guoguang Lin

In this paper,we consider a class of generalized nonlinear Kirchhoff-Sine-Gordon equation in n dimensional space.We first prove the squeezing property of the nonlinear semigroup associated with this equation and the existence of exponential attractors.Then using the Hadamards graph transformation method,the existence of inertial manifolds of the equation is obtained when N is sufficiently large. 



2015 ◽  
Vol 17 (02) ◽  
pp. 1350035 ◽  
Author(s):  
Ioan I. Vrabie

We consider the delay differential equation u′(t) ∈ Au(t) + f(t, ut), t ∈ ℝ+, where A is the infinitesimal generator of a nonlinear semigroup of contractions in a Banach space X and f is continuous, subjected to a general mixed nonlocal + local initial condition of the form u(t) = g(u)(t) + ψ(t), t ∈ [-τ, 0]. We prove that under natural conditions on A, f, g and ψ the problem above has at least one C0-solution. Applications to T-periodic and to T-anti-periodic problems, as well as an illustrative example referring to the nonlinear diffusion equation are also included.



2012 ◽  
Vol 55 (4) ◽  
pp. 882-889
Author(s):  
Song Xueli ◽  
Peng Jigen

AbstractLp stability and exponential stability are two important concepts for nonlinear dynamic systems. In this paper, we prove that a nonlinear exponentially bounded Lipschitzian semigroup is exponentially stable if and only if the semigroup is Lp stable for some p > 0. Based on the equivalence, we derive two sufficient conditions for exponential stability of the nonlinear semigroup. The results obtained extend and improve some existing ones.



2008 ◽  
Vol 9 (5) ◽  
pp. 1905-1917 ◽  
Author(s):  
Chintha Nandanie Shanthidevi ◽  
Toshitaka Matsumoto ◽  
Shinnosuke Oharu


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