Exponential Stability Estimate of Fully Nonlinear Aceive Equation by Boundary Control
The well-posed problem for the fully nonlinear Aceive diffusion and dispersion equation on the domain [0, 1] is investigated by using boundary control. The existence and uniqueness of the solutions with the help of the Banach fixed point theorem and the theory of operator semigroups are verified. By using some inequalities and integration by parts, the exponential stability of the fully nonlinear Aceive diffusion and dispersion equation with the designed boundary feedback is also proved.
D. C. Lu and R. Y. Zhu, "Exponential Stability Estimate of Fully Nonlinear Aceive Equation by Boundary Control", Key Engineering Materials, Vols. 467-469, pp. 1078-1083, 2011