一类半线性退化抛物方程在边界控制函数作用下的近似能控性

用Kakutani不动点定理证明一类一维的半线性退化抛物方程在边界控制函数作用下的近似能控性, 其中该方程的控制函数作用在退化点x=0处, 边界条件为极限意义下的第二类边界条件, 在非退化点x=1处边界条件为齐次Dirichlet条件.

Approximate Controllability of a Class of Semilinear Degenerate Parabolic Equations with Boundary Control Functions

We proved the approximate controllability of a class of one-dimensional semilinear degenerate parabolic equations with boundary control functions by using the Kakutani fixed point theorem. The boundary condition of the problem at the degenerate point x=0 to be controlled is the second boundary condition in the sense of limit, and the boundary condition is the homogeneous Dirichlet condition at the non degenerate point x=1.