Controllability Under Positive Constraints for Quasilinear Parabolic PDEs

TL;DR

This paper investigates the controllability of a class of nonlinear parabolic PDEs with positive constraints, establishing minimal control time and extending controllability results to various initial and target states.

Contribution

It provides the first global steady state controllability result for quasilinear parabolic PDEs with nonlinear diffusion under positive constraints.

Findings

Minimal controllability time is strictly positive.

Global steady state controllability is achieved under constraints.

Controllability extends to any initial and target states.

Abstract

This paper deals with the analysis of the internal control with constraint of positive kind of a parabolic PDE with nonlinear diffusion when the time horizon is large enough. The minimal controllability time will be strictly positive. We prove a global steady state constrained controllability result for a quasilinear parabolic with nonlinearity in the diffusion term. Then, under suitable dissipative assumption in the system and local controllability results, we conclude the result to any initial datum and any target trajectory.