scholarly journals Polynomial Decay Rate for Kirchhoff Type in Viscoelasticity with Logarithmic Nonlinearity and Not Necessarily Decreasing Kernel

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 226 ◽  
Author(s):  
Salah Boulaaras ◽  
Alaeddin Draifia ◽  
Mohammad Alnegga
Keyword(s):  
Decay Rate ◽  
Global Solution ◽  
Polynomial Decay ◽  
Asymptotically Stable ◽  
Kirchhoff Type ◽  
Stable Result

This paper describes a polynomial decay rate of the solution of the Kirchhoff type in viscoelasticity with logarithmic nonlinearity, where an asymptotically-stable result of the global solution is obtained taking into account that the kernel is not necessarily decreasing.

scholarly journals Asymptotic behavior for a viscoelastic Kirchhoff equation with distributed delay and Balakrishnan–Taylor damping

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Abdelbaki Choucha ◽  
Salah Boulaaras
Keyword(s):  
Asymptotic Behavior ◽  
Decay Rate ◽  
Energy Method ◽  
Distributed Delay ◽  
Type Equation ◽  
General Decay ◽  
Kirchhoff Equation ◽  
General Decay Rate ◽  
Kirchhoff Type ◽  
Nonlinear Viscoelastic

AbstractA nonlinear viscoelastic Kirchhoff-type equation with Balakrishnan–Taylor damping and distributed delay is studied. By the energy method we establish the general decay rate under suitable hypothesis.

scholarly journals Optimal Polynomial Decay to Coupled Wave Equations and Its Numerical Properties

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
R. F. C. Lobato ◽  
S. M. S. Cordeiro ◽  
M. L. Santos ◽  
D. S. Almeida Júnior
Keyword(s):  
Decay Rate ◽  
Spectral Methods ◽  
Finite Differences ◽  
Wave Equations ◽  
Coupled System ◽  
Polynomial Decay ◽  
One Dimensional ◽  
Coupled Wave Equations ◽  
Optimal Polynomial ◽  
The One

In this work we consider a coupled system of two weakly dissipative wave equations. We show that the solution of this system decays polynomially and the decay rate is optimal. Computational experiments are conducted in the one-dimensional case in order to show that the energies properties are preserved. In particular, we use finite differences and also spectral methods.

Decay of solutions to a two-layer quasi-geostrophic model

2017 ◽  
Vol 15 (04) ◽  
pp. 595-606 ◽  
Author(s):  
Boling Guo ◽  
Daiwen Huang ◽  
Jingjun Zhang
Keyword(s):  
Fluid Dynamics ◽  
Galerkin Method ◽  
Decay Rate ◽  
Global Solution ◽  
Initial Value Problem ◽  
Splitting Method ◽  
Geophysical Fluid Dynamics ◽  
Initial Value ◽  
Decay Of Solutions

We consider a two-layer quasi-geostrophic model in geophysical fluid dynamics. By Faedo–Galerkin method and asymptotic argument, we prove the existence of the global solution to the initial value problem of this model in [Formula: see text]. Moreover, using the Fourier splitting method, we also obtain the decay rate of the solutions.

scholarly journals Lower bound of decay rate for higher-order derivatives of solution to the compressible fluid models of Korteweg type

2020 ◽  
Vol 71 (4) ◽  
Author(s):  
Jincheng Gao ◽  
Zeyu Lyu ◽  
Zheng-an Yao
Keyword(s):  
Lower Bound ◽  
Decay Rate ◽  
Global Solution ◽  
Three Dimensional ◽  
Low Frequency ◽  
Navier Stokes ◽  
Whole Space ◽  
Spatial Derivatives ◽  
State 1 ◽  
Derivatives Of

Abstract This paper concerns the lower bound decay rate of global solution for compressible Navier–Stokes–Korteweg system in three-dimensional whole space under the $$H^{4}\times H^{3}$$ H 4 × H 3 framework. At first, the lower bound of decay rate for the global solution converging to constant equilibrium state (1, 0) in $$L^2$$ L 2 -norm is $$(1+t)^{-\frac{3}{4}}$$ ( 1 + t ) - 3 4 if the initial data satisfy some low-frequency assumption additionally. Furthermore, we also show that the lower bound of the $$k(k\in [1, 3])$$ k ( k ∈ [ 1 , 3 ] ) th-order spatial derivatives of solution converging to zero in $$L^2$$ L 2 -norm is $$(1+t)^{-\frac{3+2k}{4}}$$ ( 1 + t ) - 3 + 2 k 4 . Finally, it is proved that the lower bound of decay rate for the time derivatives of density and velocity converging to zero in $$L^2$$ L 2 -norm is $$(1+t)^{-\frac{5}{4}}$$ ( 1 + t ) - 5 4 .

Sign in / Sign up

Export Citation Format

Share Document