Null controllability of degenerate parabolic cascade systems

Abstract

Abstract. In this paper, we study the null controllability of degenerate semilinear cas-cade parabolic systems with one control force. The key tool is the Carleman estimatesdeveloped recently for degenerate one dimension parabolic equations. We develop a Carle-man estimate for these systems and then an observability inequality for the linear adjointsystem. We conclude by linearization and fixed point arguments. Portugaliae Mathemat-ica .Keywords.semigroups, Carleman estimates, degenerate parabolic equations, Cascade,observability inequality, null controllability.Mathematics Subject Classi cation (2000). 35K05, 35K65, 93C20 1. Introduction This paper is concerned with null controllability for the following coupled degeneratesemilinear cascade parabolic system u t − ( a 1 ( x ) u x ) x + F 1 ( t,x,u ) = h ( t,x )1 ω , ( t,x ) ∈ (0 ,T ) × (0 , 1) , (1) v t − ( a 2 ( x ) v x ) x + F 2 ( t,x,u,v ) = 0 , ( t,x ) ∈ (0 ,T ) × (0 , 1) , (2) u ( t, 0) = u ( t, 1) = v ( t, 0) = v ( t, 1) = 0 , t∈