Approximate Controllability Of Quasi-Linear Parabolic Equations With Nonnegative Constraint

Controllability is one of fundamental issues in mathematical control theory,which is mainly concerned with feasibility problems,that is,whether a system can reach or approach an expected goal through the action of a control.In practical problems,control generally is restricted and certain constraints need to be proposed for it.This will bring difficulties to the study of controllability.This dissertation is mainly devoted to studying the approximate con-trollability of a class of multi-dimensional quasi-linear parabolic equations with nonnegative control constraint,and characterizing the set of targets,which can be approximately control-lable under nonnegative control.The existing results in this respect mainly focus on some special one-dimensional quasi-linear parabolic equations.The method in the proof of the main result in this dissertation is the fixed point technique.The key is to establish the constrained controllability of the linearized parabolic system by using the variational method and give the cost estimate for the nonnegative control in the L~p-space.