Feedback exponential stabilization of the semilinear heat equation with nonlocal initial conditions

Abstract

The present paper is devoted to the problem of stabilization of the one-dimensional semilinear heat equation with nonlocal initial conditions. The control is with boundary actuation. It is linear, of finite-dimensional structure, given in an explicit form. It allows to write the corresponding solution of the closed-loop equation in a mild formulation via a kernel, then to apply a fixed point argument in a convenient space.

Keywords

• exponential stabilization
• parabolic equations
• nonlocal initial conditions
• feedback control
• contraction mapping theorem