Asymptotic stability for nonlinear PDEs with hysteresis

1994 ◽  
Vol 5 (1) ◽  
pp. 39-56 ◽  
Author(s):  
Nobuyuki Kenmochi ◽  
Augusto Visintin
Keyword(s):  
Periodic Solution ◽  
Asymptotic Stability ◽  
Evolution Equations ◽  
Stable Equilibrium ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Nonlinear Pdes ◽  
Independent Function ◽  
Forcing Term ◽  
Stability Of The Solution

Nonlinear evolution equations including hysteresis functionals are studied. It is the purpose of this paper to investigate the asymptotic stability of the solution as time t → + ∞. In the case when the forcing term of the equation tends to a time-independent function as t → + ∞, we shall show that the solution stabilizes at + ∞ and the system is asymptotically stable (equilibrium stability). In the case when the forcing term is periodic in time, we shall show that there is at least one periodic solution and that in some restricted cases the periodic solution is unique.

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.

scholarly journals The(G'/G,1/G)-Expansion Method and Its Applications for Solving Two Higher Order Nonlinear Evolution Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-20 ◽  
Author(s):  
E. M. E. Zayed ◽  
K. A. E. Alurrfi
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Higher Order ◽  
Nonlinear Evolution Equations ◽  
Nonlinear Pdes ◽  
Mathematical Tool ◽  
Wave Solutions ◽  
Klein Gordon

The two variable(G'/G,1/G)-expansion method is employed to construct exact traveling wave solutions with parameters of two higher order nonlinear evolution equations, namely, the nonlinear Klein-Gordon equations and the nonlinear Pochhammer-Chree equations. When the parameters are replaced by special values, the well-known solitary wave solutions of these equations are rediscovered from the traveling waves. This method can be thought of as the generalization of well-known original(G'/G)-expansion method proposed by Wang et al. It is shown that the two variable(G'/G,1/G)-expansion method provides a more powerful mathematical tool for solving many other nonlinear PDEs in mathematical physics.

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

New Integrable Nonlinear Evolution Equations

1979 ◽  
Vol 47 (5) ◽  
pp. 1698-1700 ◽  
Author(s):  
Miki Wadati ◽  
Kimiaki Konno ◽  
Yoshi H. Ichikawa
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations
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