Unique continuation and observability for a semi-linear parabolic system

Abstract

This article is concerned with the unique continuation and observability of a semi-linear parabolic system in a bounded domain Ω with homogeneous Dirichlet boundary conditions. We first study the existence and uniqueness of the L∞-solution to the system when the initial value belongs to L∞(Ω)2. We then build up some observation estimates for this system. As a consequence, we can conclude if two solutions are equal over a nonempty open subset ω ⊂ Ω at some time T > 0, then they coincide over Ω × [0, T].