Dynamical Systems Method for ill - posed equations with monotone operators ∗
نویسنده
چکیده
Consider an operator equation (*) B(u) − f = 0 in a real Hilbert space. Let us call this equation ill-posed if the operator B (u) is not boundedly invertible, and well-posed otherwise. The DSM (dynamical systems method) for solving equation (*) consists of a construction of a Cauchy problem, which has the following properties: 1) it has a global solution for an arbitrary initial data, 2) this solution tends to a limit as time tends to infinity, 3) the limit is the minimal-norm solution to the equation B(u) = f. A global convergence theorem is proved for DSM for equation (*) with monotone C 2 loc operators B.
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