On a continuous analog of the gradient method

In a real Hilbert space $H$ we consider the nonlinear operator equation $P(x)=0$ and the continuous gradient method
\begin{equation} x'(t)=-P'(x)*P(x),\qquad x(0)=x_0. \tag{*} \end{equation}
Two theorems on the convergence of the process (*) to the solution of the equation $P(x)=0$ are proved.