Matthew A. Fury
In this article, we consider the nonautonomous evolution problem with initial condition where -A generates a holomorphic semigroup of angle on a Banach space X and . The problem is generally ill-posed under such conditions, and so we employ methods to approximate known solutions of the problem. In particular, we prove the existence of a family of regularizing operators for the problem which stems from the solution of an approximate well-posed problem. In fact, depending on whether or , we provide two separate approximations each yielding a regularizing family. The theory has applications to ill-posed partial differential equations in , where A is a strongly elliptic differential operator and is a fixed domain in .
Submitted November 3, 2012. Published April 11, 2013.
Math Subject Classifications: 46B99, 47D06.
Key Words: Regularizing family of operators; ill-posed evolution equation; holomorphic semigroup; strongly elliptic operator.
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| Matthew Fury |
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