NULL BOUNDARY CONTROLLABILITY FOR SOME BIOLOGICAL AND CHEMICAL DIFFUSION PROBLEMS

Abstract

. We examine the null boundary controllability of diffusion problems (with non-local boundary conditions) arising from the morphogen concentration process and the electrochemistry. Two different types of semi-periodic conditions are addressed. Also, towards further applications to biological and chemical diffusion problems, we comment on anti-semi-periodic boundary conditions. Such boundary conditions make the auxiliary spectral problems nonself-adjoint and, therefore the classical eigenfunctions expansion method does not work. The systems of eigenfunctions form a Riesz basis in the L2 space by adding associated eigenfunctions. For the controllability, we determine the admissible classes of initial data in terms of their Fourier coefficients. Finally, we present the null boundary controllability of these problems by the reduction to the moment problem.