Dynamics of a Higher-Order Ginzburg–Landau-Type Equation

2021 ◽  
pp. 187-207
Author(s):  
Theodoros P. Horikis ◽  
Nikos I. Karachalios ◽  
Dimitrios J. Frantzeskakis
Keyword(s):  
Type Equation ◽  
Higher Order ◽  
Ginzburg Landau

scholarly journals Global Attractors for the Higher-Order Evolution Equation

2020 ◽  
Vol 5 (1) ◽  
pp. 195-210
Author(s):  
Erhan Pişkin ◽  
Hazal Yüksekkaya
Keyword(s):  
Asymptotic Behavior ◽  
Evolution Equation ◽  
Global Solution ◽  
Global Attractor ◽  
Type Equation ◽  
Global Attractors ◽  
Higher Order ◽  
Evolution Type

AbstractIn this paper, we obtain the existence of a global attractor for the higher-order evolution type equation. Moreover, we discuss the asymptotic behavior of global solution.

scholarly journals Cauchy problem for the complex Ginzburg-Landau type Equation with $L^{p}$-initial data

2014 ◽  
Vol 139 (2) ◽  
pp. 353-361 ◽  
Author(s):  
Daisuke Shimotsuma ◽  
Tomomi Yokota ◽  
Kentarou Yoshii
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Type Equation ◽  
Ginzburg Landau

scholarly journals Dynamical playground of a higher-order cubic Ginzburg-Landau equation: From orbital connections and limit cycles to invariant tori and the onset of chaos

2016 ◽  
Vol 94 (1) ◽  
Author(s):  
V. Achilleos ◽  
A. R. Bishop ◽  
S. Diamantidis ◽  
D. J. Frantzeskakis ◽  
T. P. Horikis ◽  
...  
Keyword(s):  
Limit Cycles ◽  
Landau Equation ◽  
Invariant Tori ◽  
Higher Order ◽  
Ginzburg Landau ◽  
Onset Of Chaos ◽  
Ginzburg Landau Equation

scholarly journals Inverse Problem for the Sobolev Type Equation of Higher Order

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1647
Author(s):  
Alyona Zamyshlyaeva ◽  
Aleksandr Lut
Keyword(s):  
Inverse Problem ◽  
Bounded Operator ◽  
Type Equation ◽  
Higher Order ◽  
Successive Approximations ◽  
Unknown Coefficient ◽  
Method Of Successive Approximations ◽  
Sobolev Type ◽  
Equivalent Problems ◽  
Sobolev Type Equation

The article investigates the inverse problem for a complete, inhomogeneous, higher-order Sobolev type equation, together with the Cauchy and overdetermination conditions. This problem was reduced to two equivalent problems in the aggregate: regular and singular. For these problems, the theory of polynomially bounded operator pencils is used. The unknown coefficient of the original equation is restored using the method of successive approximations. The main result of this work is a theorem on the unique solvability of the original problem. This study continues and generalizes the authors’ previous research in this area. All the obtained results can be applied to the mathematical modeling of various processes and phenomena that fit the problem under study.

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