Stabilization of the Korteweg-de Vries-Burgers equation with non-periodic boundary feedbacks

2003 ◽  
Vol 11 (1-2) ◽  
pp. 81-108 ◽  
Author(s):  
Mohammed Aassila
Keyword(s):  
Periodic Boundary ◽  
Burgers Equation ◽  
De Vries

scholarly journals On Monotonic Pattern in Periodic Boundary Solutions of Cylindrical and Spherical Kortweg–De Vries–Burgers Equations

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 220
Author(s):  
Alexey Samokhin
Keyword(s):  
Periodic Boundary ◽  
Asymptotic Formulas ◽  
Burgers Equations ◽  
Spherical Waves ◽  
Constant Height ◽  
De Vries ◽  
Spatial Dimensions ◽  
Integral Characteristics ◽  
Boundary Solutions ◽  
Shock Fronts

We studied, for the Kortweg–de Vries–Burgers equations on cylindrical and spherical waves, the development of a regular profile starting from an equilibrium under a periodic perturbation at the boundary. The regular profile at the vicinity of perturbation looks like a periodical chain of shock fronts with decreasing amplitudes. Further on, shock fronts become decaying smooth quasi-periodic oscillations. After the oscillations cease, the wave develops as a monotonic convex wave, terminated by a head shock of a constant height and equal velocity. This velocity depends on integral characteristics of a boundary condition and on spatial dimensions. In this paper the explicit asymptotic formulas for the monotonic part, the head shock and a median of the oscillating part are found.

The step-decay problem for the Korteweg-de Vries-Burgers equation

1991 ◽  
Vol 25 (1) ◽  
pp. 16-25 ◽  
Author(s):  
P. I. Naumkin ◽  
I. A. Shishmarev
Keyword(s):  
Burgers Equation ◽  
De Vries

Cylindrical and Spherical Dust-Ion Acoustic Solitary Waves by Damped Korteweg-de Vries-Burgers Equation

2019 ◽  
Vol 49 (5) ◽  
pp. 693-697 ◽  
Author(s):  
Dong-Ning Gao ◽  
Zheng-Rong Zhang ◽  
Jian-Peng Wu ◽  
Dan Luo ◽  
Wen-Shan Duan ◽  
...  
Keyword(s):  
Solitary Waves ◽  
Burgers Equation ◽  
Ion Acoustic Solitary Waves ◽  
Ion Acoustic ◽  
De Vries
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