Global existence and asymptotic decay of solutions to the nonlinear Timoshenko system with memory

2013 ◽  
Vol 84 ◽  
pp. 1-17 ◽  
Author(s):  
Yongqin Liu ◽  
Shuichi Kawashima
Keyword(s):  
Global Existence ◽  
Timoshenko System ◽  
Asymptotic Decay ◽  
Decay Of Solutions ◽  
With Memory

Global existence and asymptotic behavior of solutions to the generalized cubic double dispersion equation

2015 ◽  
Vol 13 (03) ◽  
pp. 233-254 ◽  
Author(s):  
Shuichi Kawashima ◽  
Yu-Zhu Wang
Keyword(s):  
Asymptotic Behavior ◽  
Global Existence ◽  
Dispersion Equation ◽  
Dimensional Space ◽  
Asymptotic Behavior Of Solutions ◽  
Initial Value ◽  
Linear Solution ◽  
Asymptotic Decay ◽  
Decay Of Solutions ◽  
Double Dispersion

In this paper, we study the initial value problem for the generalized cubic double dispersion equation in n-dimensional space. Under a small condition on the initial data, we prove the global existence and asymptotic decay of solutions for all space dimensions n ≥ 1. Moreover, when n ≥ 2, we show that the solution can be approximated by the linear solution as time tends to infinity.

scholarly journals Global existence and asymptotic decay of solutions to the non-isentropic Euler–Maxwell system

2014 ◽  
Vol 24 (14) ◽  
pp. 2851-2884 ◽  
Author(s):  
Yue-Hong Feng ◽  
Shu Wang ◽  
Shuichi Kawashima
Keyword(s):  
Global Existence ◽  
Charge Transport ◽  
Smooth Solution ◽  
Maxwell Equations ◽  
Maxwell System ◽  
Time Decay ◽  
Asymptotic Decay ◽  
Decay Of Solutions ◽  
Compressible Euler ◽  
Time Decay Rate

The non-isentropic compressible Euler–Maxwell system is investigated in ℝ3 in this paper, and the Lq time decay rate for the global smooth solution is established. It is shown that the density and temperature of electron converge to the equilibrium states at the same rate [Formula: see text] in Lq norm. This phenomenon on the charge transport shows the essential relation of the equations with the non-isentropic Euler–Maxwell and the isentropic Euler–Maxwell equations.

Global existence, asymptotic behavior and uniform attractor for a non-autonomous Timoshenko system of type III with weak damping

2020 ◽  
pp. 1-25
Author(s):  
Yuming Qin ◽  
Ye Sheng
Keyword(s):  
Global Existence ◽  
Existence Of Solutions ◽  
Semigroup Theory ◽  
Uniform Attractor ◽  
Timoshenko System ◽  
One Dimensional ◽  
Type Iii ◽  
Global Existence Of Solutions ◽  
Decay Of Solutions ◽  
Weak Damping

In this paper, we investigate one-dimensional thermoelastic system of Timoshenko type III with double memory dampings. At first we give the global existence of solutions by using semigroup theory. Then we can prove the energy decay of solutions by constructing a series of Lyapunov functionals and obtain the existence of absorbing ball. Finally, we prove the asymptotic compactness by using uniform contractive functions and obtain the existence of uniform attractor.

Global existence, nonexistence, and decay of solutions for a wave equation of p-Laplacian type with weak and p-Laplacian damping, nonlinear boundary delay and source terms

2021 ◽  
pp. 1-16
Author(s):  
Nouri Boumaza ◽  
Billel Gheraibia
Keyword(s):  
Global Existence ◽  
Nonlinear Boundary ◽  
Blow Up ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Asymptotic Behavior Of Solutions ◽  
Source Terms ◽  
Delay Term ◽  
Laplacian Equation ◽  
Decay Of Solutions

In this paper, we consider the initial boundary value problem for the p-Laplacian equation with weak and p-Laplacian damping terms, nonlinear boundary, delay and source terms acting on the boundary. By introducing suitable energy and perturbed Lyapunov functionals, we prove global existence, finite time blow up and asymptotic behavior of solutions in cases p > 2 and p = 2. To our best knowledge, there is no results of the p-Laplacian equation with a nonlinear boundary delay term.

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