Null controllability of the advection-dispersion equation with respect to the dispersion parameter using the Fokas method

Abstract

We investigate the null controllability of the linear advection-dispersion (LAD) equation posed on a finite interval. To this end, we employ the Fokas method to determine boundary controls and the controlled solutions concerning varying dispersion parameters and final times. By employing the Fokas method for the LAD equation, which provides an explicit integral representation of the solution, we enable a comprehensive analysis of null controllability. Consequently, we derive a boundary control input that effectively steers the solution from its initial state to the zero state within a given final time. The proposed approach offers a straightforward means to achieve the null controllability for the LAD equation, even as the dispersion parameter and the final time vary. Importantly, the effectiveness of this approach can be extended to various types of boundary control problems, thereby enhancing its broader applicability and potential impact.