scholarly journals The Rate at Which the Energy of Solutions for a Class ofp-Laplacian Wave Equation Decays

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
Soufiane Mokeddem ◽  
Khaled Ben Walid Mansour

We will investigate the decay estimate of the energy of the global solutions to thep-Laplacian wave equation with dissipation of the formutt-div (∇xup-2∇xu)+σ(t)(ut-div (∇xutm-2∇xut))=0under suitable assumptions on the positive functionσ. For this end we use the multiplier method combined with nonlinear integral inequalities given by Martinez; the proof is based on the construction of a special weight function that depends on the behavior ofσ.

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Banyat Sroysang

Sulaiman presented, in 2008, new kinds of Hardy-Hilbert’s integral inequality in which the weight function is homogeneous. In this paper, we present a generalization on the kinds of Hardy-Hilbert’s integral inequality.


2018 ◽  
Vol 59 (6) ◽  
pp. 061503 ◽  
Author(s):  
Runzhang Xu ◽  
Xingchang Wang ◽  
Yanbing Yang ◽  
Shaohua Chen

2007 ◽  
Vol 2007 ◽  
pp. 1-9 ◽  
Author(s):  
Yaojun Ye

This paper studies the existence of global solutions to the initial-boundary value problem for some nonlinear degenerate wave equations by means of compactness method and the potential well idea. Meanwhile, we investigate the decay estimate of the energy of the global solutions to this problem by using a difference inequality.


2013 ◽  
Vol 405-408 ◽  
pp. 3160-3164
Author(s):  
Yao Jun Ye

The initial-boundary value problem for a class of nonlinear Petrovsky systems in bounded domain is studied. We prove the energy decay estimate of global solutions through the use of a difference inequality.


2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Daewook Kim ◽  
Dojin Kim ◽  
Keum-Shik Hong ◽  
Il Hyo Jung

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.


1995 ◽  
Vol 62 (2) ◽  
pp. 155-172
Author(s):  
XS. Feng ◽  
F. Wei

2009 ◽  
Vol 40 (3) ◽  
pp. 217-223 ◽  
Author(s):  
Bicheng Yang

In this paper, by using the way of weight function and the technic of real analysis, a new integral inequality with some parameters and a best constant factor is given, which is a relation to two basic Hilbert-type integral inequalities. The equivalent form and the reverse forms are considered.


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