Chapter 1 The Cauchy problem for an infinite one dimensional system of particles with nonlinear viscoelastic ties

2000 ◽  
Keyword(s):  
Cauchy Problem ◽  
Dimensional System ◽  
One Dimensional ◽  
Nonlinear Viscoelastic ◽  
System Of Particles ◽  
The Cauchy Problem

scholarly journals Global Existence and Decay for a System of Two Singular Nonlinear Viscoelastic Equations with General Source and Localized Frictional Damping Terms

2020 ◽  
Vol 2020 ◽  
pp. 1-15 ◽  
Author(s):  
Salah Mahmoud Boulaaras ◽  
Rafik Guefaifia ◽  
Nadia Mezouar ◽  
Ahmad Mohammed Alghamdi
Keyword(s):  
Boundary Condition ◽  
Lyapunov Functional ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Dimensional System ◽  
One Dimensional ◽  
Nonlinear Viscoelastic ◽  
Frictional Damping ◽  
Viscoelastic Equations ◽  
General Source

The current paper deals with the proof of a global solution of a viscoelasticity singular one-dimensional system with localized frictional damping and general source terms, taking into consideration nonlocal boundary condition. Moreover, similar to that in Boulaaras’ recent studies by constructing a Lyapunov functional and use it together with the perturbed energy method in order to prove a general decay result.

THE NUMERICAL SOLUTION OF THE BOLTZMANN KINETIC EQUATION FOR GRANULAR GASES

2019 ◽  
pp. 25-30
Author(s):  
I. Gapyak
Keyword(s):  
Cauchy Problem ◽  
Kinetic Equation ◽  
Numerical Solution ◽  
Dimensional Space ◽  
Boltzmann Kinetic Equation ◽  
Granular Gases ◽  
Two Dimensional ◽  
System Of Particles ◽  
The Cauchy Problem

For a system of particles with a dissipative interaction we consider the Boltzmann type kinetic equation for granular gases. A numerical solution of the Cauchy problem for the Boltzmann type kinetic equation is constructed in two dimensional space and its stability is investigated.

scholarly journals On the blow-up of the Cauchy problem of higher-order nonlinear viscoelastic wave equation

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Mohammad Kafini
Keyword(s):  
Cauchy Problem ◽  
Wave Equation ◽  
Blow Up ◽  
Initial Energy ◽  
Higher Order ◽  
Viscoelastic Wave Equation ◽  
Nonlinear Viscoelastic ◽  
Viscoelastic Wave ◽  
The Cauchy Problem ◽  
Whole Space

<p style='text-indent:20px;'>In this paper we consider the Cauchy problem for a higher-order viscoelastic wave equation with finite memory and nonlinear logarithmic source term. Under certain conditions on the initial data with negative initial energy and with certain class of relaxation functions, we prove a finite-time blow-up result in the whole space. Moreover, the blow-up time is estimated explicitly. The upper bound and the lower bound for the blow up time are estimated.</p>

scholarly journals Global existence of small amplitude solutions to one-dimensional nonlinear Klein–Gordon systems with different masses

2015 ◽  
Vol 12 (04) ◽  
pp. 745-762 ◽  
Author(s):  
Donghyun Kim
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Small Amplitude ◽  
Space Dimension ◽  
Structural Condition ◽  
Cauchy Data ◽  
One Dimensional ◽  
Compactly Supported ◽  
The Cauchy Problem ◽  
Klein Gordon

We study the Cauchy problem for systems of cubic nonlinear Klein–Gordon equations with different masses in one space dimension. Under a suitable structural condition on the nonlinearity, we will show that the solution exists globally and decays of the rate [Formula: see text] in [Formula: see text], [Formula: see text] as [Formula: see text] tends to infinity even in the case of mass resonance, if the Cauchy data are sufficiently small, smooth and compactly supported.

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