Adaptive Boundary Control for the Dynamics of the Generalized Burgers-Huxley Equation

作     者：Zaki Mrzog Alaofi Talaat Sayed Ali Faisal Abd Alaal Silvestru Sever Dragomir Zaki Mrzog Alaofi;Talaat Sayed Ali;Faisal Abd Alaal;Silvestru Sever Dragomir

作者机构：Department of Mathematics College of Science and Arts King Khalid University Muhayil Asir Saudia Arabia Mathematics College of Engineering & Science Victoria University Melbourne Australia Department of Mathematics and Computer Science Faculty of Science Menoufia University Shebeen El-Kom Egypt Department of Mathematics Faculty of Science Damanhour University Damanhour Egypt 

出 版 物：《Open Journal of Applied Sciences》 (应用科学（英文）)

年 卷 期：2022年第12卷第8期

页      面：1416-1438页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Adaptive Boundary Control Generalized Burgers-Huxley Equation Stability Adomian Decomposition Method 

摘      要：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.