Global convergence for ill-posed equations with monotone operators: the dynamical systems method
نویسنده
چکیده
Consider an operator equation F(u) = 0 in a real Hilbert space. Let us call this equation ill-posed if the operator F ′(u) is not boundedly invertible, and well-posed otherwise. If F is monotone C2 loc(H) operator, then we construct 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 and (3) the limit is the minimum norm solution to the equation F(u) = 0. An example of applications to linear ill-posed operator equation is given. PACS numbers: 02.60.−x, 02.30.Zz Mathematics Subject Classification: 34r30, 35r25, 35r30, 37c35, 37l05, 37n30, 47a52, 47j06, 65m30, 65n21
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