American Institute of Mathematical Sciences

• Previous Article
Complete controllability for a class of fractional evolution equations with uncertainty
• EECT Home
• This Issue
• Next Article
Controllability of Hilfer fractional integro-differential equations of Sobolev-type with a nonlocal condition in a Banach space
doi: 10.3934/eect.2020086

Solvability in abstract evolution equations with countable time delays in Banach spaces: Global Lipschitz perturbation

 Department of Mathematics, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan

* Corresponding author: Tomomi Yokota

Received  February 2020 Revised  June 2020 Published  August 2020

Fund Project: The first author is supported by Grant-in-Aid for Scientific Research (C), No. 16K05182

This paper deals with the solvability in the semilinear abstract evolution equation with countable time delays,
 $\begin{equation*} \begin{cases} \dfrac{du}{dt}(t)+Au(t) = F(u(t), (u(t-\tau_n))_{n\in\mathbb{N}}), & t>0, \\ u(t) = u_0(t), & t \in \bigcup\limits_{n \in \mathbb{N}}[-\tau_n,0], \end{cases} \end{equation*}$
in a Banach space
 $X$
, where
 $-A$
is a generator of a
 $C_0$
-semigroup with exponential decay and
 $F: X \times X^\mathbb{N} \to X$
is Lipschitz continuous. Nicaise and Pignotti (J. Evol. Equ.; 2018;18;947–971) established global existence and exponential decay in time for solutions of the above equation with finite time delays in Hilbert spaces under global or local Lipschitz conditions. The purpose of the present paper is to generalize the result to the case of countable time delays in Banach spaces under a global Lipschitz condition.
Citation: Tomomi Yokota, Kentarou Yoshii. Solvability in abstract evolution equations with countable time delays in Banach spaces: Global Lipschitz perturbation. Evolution Equations & Control Theory, doi: 10.3934/eect.2020086
References:

show all references

References:
 [1] Xin Zhong. Global strong solution and exponential decay for nonhomogeneous magnetohydrodynamic equations. Discrete & Continuous Dynamical Systems - B, 2021, 26 (7) : 3563-3579. doi: 10.3934/dcdsb.2020246 [2] Pengyu Chen. Periodic solutions to non-autonomous evolution equations with multi-delays. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 2921-2939. doi: 10.3934/dcdsb.2020211 [3] Yongqiang Fu, Xiaoju Zhang. Global existence and asymptotic behavior of weak solutions for time-space fractional Kirchhoff-type diffusion equations. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021091 [4] Harumi Hattori, Aesha Lagha. Global existence and decay rates of the solutions for a chemotaxis system with Lotka-Volterra type model for chemoattractant and repellent. Discrete & Continuous Dynamical Systems, 2021  doi: 10.3934/dcds.2021071 [5] Quan Hai, Shutang Liu. Mean-square delay-distribution-dependent exponential synchronization of chaotic neural networks with mixed random time-varying delays and restricted disturbances. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 3097-3118. doi: 10.3934/dcdsb.2020221 [6] Pengyu Chen, Xuping Zhang, Zhitao Zhang. Asymptotic behavior of time periodic solutions for extended Fisher-Kolmogorov equations with delays. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021103 [7] Lin Yang, Yejuan Wang, Tomás Caraballo. Regularity of global attractors and exponential attractors for $2$D quasi-geostrophic equations with fractional dissipation. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021093 [8] Chenjie Fan, Zehua Zhao. Decay estimates for nonlinear Schrödinger equations. Discrete & Continuous Dynamical Systems, 2021, 41 (8) : 3973-3984. doi: 10.3934/dcds.2021024 [9] Manoel J. Dos Santos, Baowei Feng, Dilberto S. Almeida Júnior, Mauro L. Santos. Global and exponential attractors for a nonlinear porous elastic system with delay term. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2805-2828. doi: 10.3934/dcdsb.2020206 [10] Marat Akhmet, Ejaily Milad Alejaily. Abstract similarity, fractals and chaos. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2479-2497. doi: 10.3934/dcdsb.2020191 [11] Simão Correia, Mário Figueira. A generalized complex Ginzburg-Landau equation: Global existence and stability results. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021056 [12] Pengyu Chen. Non-autonomous stochastic evolution equations with nonlinear noise and nonlocal conditions governed by noncompact evolution families. Discrete & Continuous Dynamical Systems, 2021, 41 (6) : 2725-3737. doi: 10.3934/dcds.2020383 [13] Demou Luo, Qiru Wang. Dynamic analysis on an almost periodic predator-prey system with impulsive effects and time delays. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 3427-3453. doi: 10.3934/dcdsb.2020238 [14] Anderson L. A. de Araujo, Marcelo Montenegro. Existence of solution and asymptotic behavior for a class of parabolic equations. Communications on Pure & Applied Analysis, 2021, 20 (3) : 1213-1227. doi: 10.3934/cpaa.2021017 [15] Jinyi Sun, Zunwei Fu, Yue Yin, Minghua Yang. Global existence and Gevrey regularity to the Navier-Stokes-Nernst-Planck-Poisson system in critical Besov-Morrey spaces. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 3409-3425. doi: 10.3934/dcdsb.2020237 [16] Vandana Sharma. Global existence and uniform estimates of solutions to reaction diffusion systems with mass transport type boundary conditions. Communications on Pure & Applied Analysis, 2021, 20 (3) : 955-974. doi: 10.3934/cpaa.2021001 [17] Miroslav Bulíček, Victoria Patel, Endre Süli, Yasemin Şengül. Existence of large-data global weak solutions to a model of a strain-limiting viscoelastic body. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021053 [18] Manil T. Mohan, Arbaz Khan. On the generalized Burgers-Huxley equation: Existence, uniqueness, regularity, global attractors and numerical studies. Discrete & Continuous Dynamical Systems - B, 2021, 26 (7) : 3943-3988. doi: 10.3934/dcdsb.2020270 [19] Tôn Việt Tạ. Strict solutions to stochastic semilinear evolution equations in M-type 2 Banach spaces. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021050 [20] Xiongxiong Bao, Wan-Tong Li. Existence and stability of generalized transition waves for time-dependent reaction-diffusion systems. Discrete & Continuous Dynamical Systems - B, 2021, 26 (7) : 3621-3641. doi: 10.3934/dcdsb.2020249

2019 Impact Factor: 0.953