Regularization for a class of ill-posed evolution problems in Banach space |
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Authors: | Matthew A Fury Rhonda J Hughes |
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Institution: | 1. Division of Science and Engineering, Penn State Abington, 1600 Woodland Road, Abington, PA, 19001, USA 2. Department of Mathematics, Bryn Mawr College, 101 N. Merion Ave, Bryn Mawr, PA, 19010, USA
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Abstract: | We study evolution equations in Banach space, and provide a general framework for regularizing a wide class of ill-posed Cauchy problems by proving continuous dependence on modeling for nonautonomous equations. We approximate the ill-posed problem by a well-posed one, and obtain H?lder-continuous dependence results that provide estimates of the error for a class of solutions under certain stabilizing conditions. For examples that include the linearized Korteweg-de Vries equation and the Schr?dinger equation in L p ,p??2, we obtain a family of regularizing operators for the ill-posed problem. This work extends to the nonautonomous case several recent results for ill-posed problems with constant coefficients. |
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