Null controllability of some nonlinear degenerate 1D parabolic equations

摘要

The main goal of the present paper is twofold: (i) to establish the well-posedness of a class of nonlinear degenerate parabolic equations and (ii) to investigate the related null controllability and de-cay rate properties. In a previous step, we consider an appropriate regularized system, where a small parameter a is involved. More precisely, the usual nonlinear term b (x) uu x is replaced by b(x)zu(x), where z = (Id. -alpha(2)A)(-1) u and A is a Poisson-Dirichlet operator. We investigate the behavior of the null con-trols and their associated states as alpha -> 0. (C) 2017 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.