11·î22Æü(ÌÚ) 15:45 -- 17:15 Alexandre G. Ramm (Kansas State University, USA) ``Dynamical Systems Method for Solving Linear and Non-linear Ill-posed Problems'' ¡ã¸¦µæȯɽÍ×»Ý(Prof. A. G. Ramm)¡ä Consider an operator equation F(u)=0 in a Hilbert space. The problem of solving this equation is ill-posed if the operator F'(u) is not boundedly invertible. A general method for solving linear and nonlinear ill-posed problems in a Hilbert space is presented. This method consists of the construction of a nonlinear dynamical system, that is, a Cauchy problem, which has the following properties: 1) it has a global solution, 2) this solution tends to a limit as time tends to infinity, 3) the limit solves the original linear or non-linear problem. New convergence and discretization theorems are obtained. Examples of the applications of this approach are given. The method works for a wide range of well-posed problems as well. A.G.Ramm: e-mail ramm@math.ksu.edu, http://www.math.ksu.edu/~ramm