Global attractor and decay estimates of solutions to a class of nonlinear evolution equations

2010 ◽  
Vol 34 (5) ◽  
pp. 497-508 ◽  
Author(s):  
Caisheng Chen ◽  
Hui Wang ◽  
ShengLan Zhu
Keyword(s):  
Global Attractor ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Decay Estimates ◽  
Estimates Of Solutions

scholarly journals Estimates of Solutions to Nonlinear Evolution Equations

2018 ◽  
Vol 14 (2) ◽  
pp. 7812-7817
Author(s):  
Alexander G. Ramm
Keyword(s):  
Banach Space ◽  
Global Solution ◽  
Nonlinear Operator ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Unique Global Solution ◽  
Estimates Of Solutions ◽  
Suitable Function

Consider the equation                  u’(t) = A (t, u (t)),   u(0)= U0 ;   u' := du/dt     (1).   Under some assumptions on the nonlinear operator A(t,u) it is proved that problem (1) has a unique global solution and this solution satisfies the following estimate                                               ||u (t)|| < µ (t) -1     for every t belongs to R+ = [0,infinity). Here µ(t) > 0,   µ belongs to  C1 (R+), is a suitable function and the norm ||u || is the norm in a Banach space X with the property ||u (t) ||’   <=  ||u’ (t) ||.

scholarly journals A Remark on the Global Attractors of the Nonlinear Evolution Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-3
Author(s):  
Chang Ya-ya ◽  
Ma Qiao-zhen
Keyword(s):  
Fractal Dimension ◽  
Global Attractor ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Global Attractors ◽  
Nonlinear Evolution Equations ◽  
Elastic Rod ◽  
Forcing Term ◽  
Nonlinear Elastic ◽  
Oscillation Equation

We study the existence of global attractor of the nonlinear elastic rod oscillation equation when the forcing term belongs only to H−1(Ω); furthermore, we prove that the fractal dimension of global attractor is finite.

Traveling wave solutions for the Couple Boiti-Leon-Pempinelli System by using extended Jacobian elliptic function expansion method

2015 ◽  
Vol 11 (3) ◽  
pp. 3134-3138 ◽  
Author(s):  
Mostafa Khater ◽  
Mahmoud A.E. Abdelrahman
Keyword(s):  
Elliptic Function ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Jacobian Elliptic Function ◽  
Function Expansion

In this work, an extended Jacobian elliptic function expansion method is pro-posed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the Couple Boiti-Leon-Pempinelli System which plays an important role in mathematical physics.

scholarly journals The unified method for abundant soliton solutions of local time fractional nonlinear evolution equations

2021 ◽  
Vol 22 ◽  
pp. 103979
Author(s):  
Nauman Raza ◽  
Muhammad Hamza Rafiq ◽  
Melike Kaplan ◽  
Sunil Kumar ◽  
Yu-Ming Chu
Keyword(s):  
Local Time ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Nonlinear Evolution Equations ◽  
The Unified Method ◽  
Unified Method

scholarly journals Motion of curves and surfaces and nonlinear evolution equations in (2+1) dimensions

1998 ◽  
Vol 39 (7) ◽  
pp. 3765-3771 ◽  
Author(s):  
M. Lakshmanan ◽  
R. Myrzakulov ◽  
S. Vijayalakshmi ◽  
A. K. Danlybaeva
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Curves And Surfaces
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