TITLE:
Adaptive Boundary Control for the Dynamics of the Generalized Burgers-Huxley Equation
AUTHORS:
Zaki Mrzog Alaofi, Talaat Sayed Ali, Faisal Abd Alaal, Silvestru Sever Dragomir
KEYWORDS:
Adaptive Boundary Control, Generalized Burgers-Huxley Equation, Stability, Adomian Decomposition Method
JOURNAL NAME:
Open Journal of Applied Sciences,
Vol.12 No.8,
August
25,
2022
ABSTRACT: This paper deals with the boundary control problem of the unforced generalized
Burgers-Huxley equation with high order nonlinearity when the spatial domain is
[0, 1]. We show that this type of equations are globally exponential stable in L2 [0, 1] under zero Dirichlet boundary conditions. We use an adaptive nonlinear
boundary controller to show the convergence of the solution to the trivial
solution and to show that it achieves global asymptotic stability in time. We
introduce numerical simulation for the controlled equation using the Adomian decomposition
method (ADM) in order to illustrate the performance of the controller.