scholarly journals General decay of the double dispersive wave equation with memory and source terms

2021 ◽  
Vol 5 (1) ◽  
pp. 1-8
Author(s):  
Mohamed Mellah ◽  
Keyword(s):  
Wave Equation ◽  
Bounded Domain ◽  
Global Solutions ◽  
Decay Rates ◽  
General Decay ◽  
Dispersive Wave ◽  
Source Terms ◽  
T Tau ◽  
With Memory ◽  
Dispersive Wave Equation

The double dispersive wave equation with memory and source terms \(u_{tt}-\Delta u-\Delta u_{tt}+\Delta^{2}u-\int_{0}^{t}g(t-\tau)\Delta^{2}u(\tau)d\tau-\Delta u_{t}=|u|^{p-2}u \) is considered in bounded domain. The existence of global solutions and decay rates of the energy are proved.

scholarly journals Global solutions and general decay for the dispersive wave equation with memory and source terms

2020 ◽  
Vol 4 (2) ◽  
pp. 116-122
Author(s):  
Mohamed Mellah ◽  
Keyword(s):  
Wave Equation ◽  
Global Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
General Decay ◽  
Dispersive Wave ◽  
Source Terms ◽  
Initial Boundary Value ◽  
With Memory ◽  
Dispersive Wave Equation

This paper concerns with the global solutions and general decay to an initial-boundary value problem of the dispersive wave equation with memory and source terms

scholarly journals General Decay Rates for a Laminated Beam with Memory

2019 ◽  
Vol 23 (5) ◽  
pp. 1227-1252 ◽  
Author(s):  
Zhijing Chen ◽  
Wenjun Liu ◽  
Dongqin Chen
Keyword(s):  
Decay Rates ◽  
General Decay ◽  
Laminated Beam ◽  
With Memory

Folded Solitary Waves and Foldons in the (2+1)-Dimensional Long Dispersive Wave Equation

2003 ◽  
Vol 58 (5-6) ◽  
pp. 280-284
Author(s):  
J.-F. Zhang ◽  
Z.-M. Lu ◽  
Y.-L. Liu
Keyword(s):  
Wave Equation ◽  
Solitary Waves ◽  
Coherent Structures ◽  
Bäcklund Transformation ◽  
Dispersive Wave ◽  
Variable Separation ◽  
New Class ◽  
Localized Structures ◽  
Dispersive Wave Equation ◽  
03.65 Ge

By means of the Bäcklund transformation, a quite general variable separation solution of the (2+1)- dimensional long dispersive wave equation: λqt + qxx − 2q ∫ (qr)xdy = 0, λrt − rxx + 2r ∫ (qr)xdy= 0, is derived. In addition to some types of the usual localized structures such as dromion, lumps, ring soliton and oscillated dromion, breathers soliton, fractal-dromion, peakon, compacton, fractal and chaotic soliton structures can be constructed by selecting the arbitrary single valued functions appropriately, a new class of localized coherent structures, that is the folded solitary waves and foldons, in this system are found by selecting appropriate multi-valuded functions. These structures exhibit interesting novel features not found in one-dimensions. - PACS: 03.40.Kf., 02.30.Jr, 03.65.Ge.

scholarly journals Global Existence and Energy Decay Rates for a Kirchhoff-Type Wave Equation with Nonlinear Dissipation

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Daewook Kim ◽  
Dojin Kim ◽  
Keum-Shik Hong ◽  
Il Hyo Jung
Keyword(s):  
Wave Equation ◽  
Existence And Uniqueness ◽  
Global Solutions ◽  
Growth Conditions ◽  
Decay Rates ◽  
Decay Estimates ◽  
Nonlinear Dissipation ◽  
Kirchhoff Type ◽  
Type Wave ◽  
Energy Decay Rates

The first objective of this paper is to prove the existence and uniqueness of global solutions for a Kirchhoff-type wave equation with nonlinear dissipation of the form under suitable assumptions on . Next, we derive decay estimates of the energy under some growth conditions on the nonlinear dissipationg. Lastly, numerical simulations in order to verify the analytical results are given.

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