Continuous dependence on modeling for nonlinear ill-posed problems |
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Authors: | Beth M. Campbell Hetrick Rhonda J. Hughes |
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Affiliation: | a Department of Mathematical Sciences, The Pennsylvania State University at Harrisburg, Middletown, PA 17057, USA b Department of Mathematics, Bryn Mawr College, Bryn Mawr, PA 19010, USA |
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Abstract: | The nonlinear ill-posed Cauchy problem , where A is a positive self-adjoint operator on a Hilbert space H, χ∈H, and h:[0,T)×H→H is a uniformly Lipschitz function, is studied in order to establish continuous dependence results for solutions to approximate well-posed problems. The authors show here that solutions of the problem, if they exist, depend continuously on solutions to corresponding approximate well-posed problems, if certain stabilizing conditions are imposed. The approximate problem is given by , v(0)=χ, for suitable functions f. The main result is that , where C and M are computable constants independent of β and 0<β<1. This work extends to the nonlinear case earlier results by the authors and by Ames and Hughes. |
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Keywords: | Abstract Cauchy problem Continuous dependence on modeling Nonlinear ill-posed problem |
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