Null Boundary Controllability for Biharmonic Heat Equation

Abstract

This paper deals with the null boundary controllability for the initial boundary value problems of the biharmonic heat equation within a finite interval. Two different types of boundary constraints are applied to the domain's boundaries. The first type involves endpoints supported by Neumann and Dirichlet boundary conditions. The second type involves endpoints supported solely by Neumann boundary conditions. Unlike the first case, the system is not always controllable in the second scenario. Therefore, this paper establishes a null boundary controllability criterion for the system based on the initial data terms, using the law of mass conservation. The null controllability problems with one boundary control are solved for both cases by reducing them to the exponential moment problem.