Approximate Controllability of the System Governed by Double Coupled Semilinear Degenerate Parabolic Equations (Communications in Mathematical Research, 2020)
This paper concerns the approximate controllability of the initial-boundary problem of double coupled semilinear degenerate parabolic equations. The equations are degenerate at the boundary, and the control functionacts in the interior of the spacial domain and acts only on one equation. Weovercome the difficulty of the degeneracy of the equations to show that theproblem is approximately controllable in $L^2$ by means of a fixed point theoremand some compact estimates. That is to say, for any initial and desired datain $L^2$, one can find a control function in $L^2$ such that the weak solution to theproblem approximately reaches the desired data in $L^2$ at the terminal time.