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Weakly closed nonlinear operators and parameter identification in parabolic equations by Tikhonov regularization. (English) Zbl 0835.65078

Summary: This paper is devoted to studying convergence rates for the Tikhonov regularization of nonlinear ill-posed problems from a geometrical point of view. Also the non-attainable case is considered.
In our theory, the weak closedness of the operator defining the equation plays a central role. We prove the weak closedness of this operator for two parameter estimation problems in parabolic equations.

MSC:

65J15 Numerical solutions to equations with nonlinear operators
47J25 Iterative procedures involving nonlinear operators
65M30 Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs
65J20 Numerical solutions of ill-posed problems in abstract spaces; regularization
35K55 Nonlinear parabolic equations
35R30 Inverse problems for PDEs
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