An abstract approximate controllability result and applications to elliptic and parabolic systems with dynamic boundary conditions

Abstract

The authors obtain an approximate controllability result for the nonlinear equation $y'+Ay+F(t,y)y=h(t)$ with the initial condition $y(0)=x$, where $x$ is the control and $A$ generates a $C_0$-semigroup in a Hilbert space. The Schauder fixed point theorem is the main tool. Then they apply their result to get approximate controllability for some classes of elliptic and parabolic problems with dynamic boundary conditions. There are 72 references, many of them referring to mathematical models in various areas where the results could be applied.