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¸¦µæÈ¯É½Í×»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