Stability and distributed control of degenerate diffusion equations

This paper is concerned with stability and control of the parabolic p-Laplace equation. The autonomous equation is shown to be asymptotically stable, while the stronger property of exponential stability is guaranteed by the presence of lower-order terms satisfying a suitable growth condition. On the basis of these results, the problem of reference tracking using a distributed control input is investigated and, in particular, two approaches are discussed: finite-time stabilization and quadratic optimal control. Numerical simulations are provided to support and illustrate the theoretical results.