Semilinear Evolution Equations in Banach Spaces with Application to Parabolic Partial Differential Equations

1993 ◽  
Vol 336 (2) ◽  
pp. 523 ◽  
Author(s):  
Samuel M. Rankin III
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Banach Spaces ◽  
Evolution Equations ◽  
Parabolic Partial Differential Equations ◽  
Partial Differential ◽  
Semilinear Evolution Equations

scholarly journals The Practical Feedback Stabilization for Evolution Equations in Banach Spaces

2021 ◽  
Vol 15 (2) ◽  
pp. 58-65
Author(s):  
Damak Hanen
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Banach Spaces ◽  
Lyapunov Functions ◽  
Uncertain Systems ◽  
Evolution Equations ◽  
Sufficient Conditions ◽  
Feedback Stabilization ◽  
Partial Differential ◽  
Infinite Dimensional

Abstract This paper investigates the notion of practical feedback stabilization of evolution equations satisfying some relaxed conditions in infinite-dimensional Banach spaces. Moreover, sufficient conditions are presented that guarantee practical stabilizability of uncertain systems based on Lyapunov functions. These results are applied to partial differential equations.

scholarly journals On the relations between some well-known methods and the projective Riccati equations

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 613-618
Author(s):  
Şamil Akçağıl
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Riccati Equations ◽  
Nonlinear Evolution Equations ◽  
Alternative Methods ◽  
Computational Techniques ◽  
Partial Differential ◽  
Traditional Methods

AbstractSolving nonlinear evolution equations is an important issue in the mathematical and physical sciences. Therefore, traditional methods, such as the method of characteristics, are used to solve nonlinear partial differential equations. A general method for determining analytical solutions for partial differential equations has not been found among traditional methods. Due to the development of symbolic computational techniques many alternative methods, such as hyperbolic tangent function methods, have been introduced in the last 50 years. Although all of them were introduced as a new method, some of them are similar to each other. In this study, we examine the following four important methods intensively used in the literature: the tanh–coth method, the modified Kudryashov method, the F-expansion method and the generalized Riccati equation mapping method. The similarities of these methods attracted our attention, and we give a link between the methods and a system of projective Riccati equations. It is possible to derive new solution methods for nonlinear evolution equations by using this connection.

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