On the Generation of Nonlinear Semigroups of Contractions and Evolution Equations on Hadamard Manifolds

2021 ◽  
Vol 18 (5) ◽  
Author(s):  
P. Ahmadi ◽  
H. Khatibzadeh ◽  
S. Mohebbi
Keyword(s):  
Evolution Equations ◽  
Hadamard Manifolds ◽  
Nonlinear Semigroups

scholarly journals Nonlinear semigroups and the existence and stability of solutions of semilinear nonautonomous evolution equations

1996 ◽  
Vol 1 (4) ◽  
pp. 351-380 ◽  
Author(s):  
Bernd Aulbach ◽  
Nguyen Van Minh
Keyword(s):  
Evolution Equations ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Stability Of Solutions ◽  
Nonlinear Operators ◽  
Nonlinear Semigroups ◽  
Evolution Semigroup ◽  
Existence And Stability ◽  
Functional Differential

This paper is concerned with the existence and stability of solutions of a class of semilinear nonautonomous evolution equations. A procedure is discussed which associates to each nonautonomous equation the so-called evolution semigroup of (possibly nonlinear) operators. Sufficient conditions for the existence and stability of solutions and the existence of periodic oscillations are given in terms of the accretiveness of the corresponding infinitesimal generator. Furthermore, through the existence of integral manifolds for abstract evolutionary processes we obtain a reduction principle for stability questions of mild solutions. The results are applied to a class of partial functional differential equations.

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.

Sign in / Sign up

Export Citation Format

Share Document