Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9702599 | Communications in Nonlinear Science and Numerical Simulation | 2005 | 6 Pages |
Abstract
Consider an operator equation B(u) â f = 0 in a real Hilbert space. Let us call this equation ill-posed if the operator Bâ²(u) is not boundedly invertible, and well-posed otherwise. The dynamical systems method (DSM) for solving this 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 B(u) â f = 0 with monotone Cloc2 operators B.
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Authors
A.G. Ramm,