Flatness for a Strongly Degenerate 1-D Parabolic Equation

2015/07/20 by Moyano, Iván
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1507.05582

Abstract

We consider the degenerate equation ∂_t f(t,x) - ∂_x ( x^α ∂_x f )(t,x) =0, on the unit interval x∈(0,1), in the strongly degenerate case α∈ [1,2) with adapted boundary conditions at x=0 and boundary control at x=1. We use the flatness approach to construct explicit controls in some Gevrey classes steering the solution from any initial datum f_0 ∈ L²(0,1) to zero in any time T\textgreater0.

Related

• Null controllability of one-dimensional parabolic equations by the flatness approach
• Existence and cost of boundary controls for a degenerate/singular parabolic equation
• Optimal regularity for degenerate parabolic equations on a flat boundary
• Regularity for quasi-linear parabolic equations with nonhomogeneous degeneracy or singularity
• Higher regularity for weak solutions to degenerate parabolic problems