Regional gradient observability for distributed semilinear parabolic systems

Abstract

In this paper, we extend the notion of regional observability of the gradient for linear systems to a class of semilinear parabolic systems. To reconstruct the gradient in the subregion of the system evolution domain, we begin with the first approach which combines the extension of the HUM method and the fixed point techniques. The analytical case is then tackled using sectorial property of the considered dynamic operator and converted to a fixed point problem. The two approaches lead to algorithms which are successfully implemented numerically and illustrated with examples and simulations.