TY - JOUR
T1 - Approximate Controllability of the System Governed by Double Coupled Semilinear Degenerate Parabolic Equations
AU - Wang , Chunpeng
AU - Xu , Fengdan
AU - Zhou , Qian
JO - Communications in Mathematical Research 
VL - 4
SP - 403
EP - 422
PY - 2020
DA - 2020/11
SN - 36
DO - http://doi.org/10.4208/cmr.2020-0061
UR - https://global-sci.org/intro/article_detail/cmr/18360.html
KW - Double coupled, degeneracy, approximate controllability.
AB - <p style="text-align: justify;">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 function
acts in the interior of the spacial domain and acts only on one equation. We
overcome the difficulty of the degeneracy of the equations to show that the
problem is approximately controllable in $L^2$ by means of a fixed point theorem
and some compact estimates. That is to say, for any initial and desired data
in $L^2$, one can find a control function in $L^2$ such that the weak solution to the
problem approximately reaches the desired data in $L^2$ at the terminal time.</p>