The linear stabilization problem of the modified generalized Korteweg–de Vries–Burgers equation (MGKdVB) is considered when the spatial variable lies in [0 , 1]. First, the existence and uniqueness of global solutions are proved. Next, the exponential stability of the equation is established in L2(0 , 1). Then, a linear adaptive boundary control is put forward. Finally, numerical simulations for both non-adaptive and adaptive problems are provided to illustrate the analytical outcomes.
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