Electron. J. Diff. Equ.,
Vol. 2013 (2013), No. 92, pp. 125.
Nonautonomous illposed evolution problems
with strongly elliptic differential operators
Matthew A. Fury
Abstract:
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 illposed 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 wellposed problem.
In fact, depending on whether
or
,
we provide two separate approximations each
yielding a regularizing family. The theory has applications to illposed
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; illposed evolution equation;
holomorphic semigroup; strongly elliptic operator.
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Matthew Fury
Division of Science & Engineering,
Penn State Abington
1600 Woodland Road Abington, PA 19001, USA
Tel: 2158817553 Fax: 2158817333
email: maf44@psu.edu

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