Rainfall infiltration: Direct and inverse problems on a linear evolution equation
Konstantinos A. Kalimeris, Leonidas Mindrinos · Evolution equations and control theory · 2025
Originating from the mathematical modeling of rainfall infiltration, we derived the solution of an initial-boundary value problem of a linear evolution partial differential equation by using the Fokas method. We present the illustration of the solutions that correspond to specific physical rainfall problems. Based on this formalism, we present a characterization for the associated null-controllability problem in the form of an integral equation. An effective algorithm yields the numerical derivation of a family of boundary controls that steer the solution to the desired flat final state. However, in some cases, the control can become arbitrarily large. To address this, we propose a regularization scheme that ensures relatively small controls.