Null boundary controllability for a fourth order parabolic equation
This paper deals with the following initial-boundary value problem for a one-dimensional fourth-order parabolic equation of the form \[ \begin{cases} w_t+w_{xxxx}=0 & \text{on }(0,1)\times (0,\infty),\\ w(0,t)=0,\;w_x(0,t)=0 & \text{for }t\geq 0,\\ w(x,0)=w_0(x) & \text{for }x\in [0,1],\\ w(1,t)=g(t),\;w_x(1,t)=h(t) & \text{for }t\geq 0.\end{cases}\tag{1} \] The goal of this paper is to study the null boundary controllability problem for (1). The author shows that if the initial data is continuous then the equation (1) is controllable.
one-dimensional fourth-order parabolic equation
scientific article; zbMATH DE number 1876797