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[[EQUATION]]-solution to the system when the initial value belongs to L[[EQUATION]](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[[EQUATION]]Ω at some time T>0, then they coincide over Ω[[EQUATION]][0,T].