2011/06/21 by Piermarco Cannarsa, Cannarsa, Piermarco, Giuseppe Floridia +1 · 4 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Electrical engineering #FOS: Mathematics #Nonlinear Partial Differential Equations #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1106.4232
openalex publication_date 2011/06/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this work we study the global approximate multiplicative controllability for the linear degenerate parabolic Cauchy-Neumann problem \arrayl vt-(a(x) vx)x =α(t,x)v in QT = (0,T)×(-1,1) [2.5ex] a(x)vx(t,x)|x=± 1 = 0 t∈ (0,T) [2.5ex] v(0,x)=v0 (x) x∈ (-1,1), array. with the bilinear control α(t,x)∈ L^∞ (QT). The problem is strongly degenerate in the sense that a∈ C1([-1,1]), positive on (-1,1), is allowed to vanish at ± 1 provided that a certain integrability condition is fulfilled. We will show that the above system can be steered in L2(Ω) from any nonzero, nonnegative initial state into any neighborhood of any desirable nonnegative target-state by bilinear static controls. Moreover, we extend the above result relaxing the sign constraint on v0.