Kenneth L. Kuttler, Ji Li, Meir Shillor
Abstract:
This work establishes the existence of measurable weak solutions to
evolution problems with randomness by proving and applying a novel theorem
on product measurability of limits of sequences of functions.
The measurability theorem is used to show that many important
existence theorems within the abstract theory of evolution inclusions or
equations have straightforward generalizations to settings that include random
processes or coefficients. Moreover, the convex set where the solutions are
sought is not fixed but may depend on the random variables.
The importance of adding randomness lies in the fact that real world processes
invariably involve randomness and variability. Thus, this work expands
substantially the range of applications of models with variational
inequalities and differential set-inclusions.
Submitted January 16, 2016. Published March 31, 2016.
Math Subject Classifications: 35R60, 60H15, 35R45, 35R70, 35S11.
Key Words: Partial differential inclusions; product measurability;
variational inequalities; measurable selection.
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Kenneth L. Kuttler Department of Mathematics Brigham Young University Provo, UT 84602, USA email: klkuttle@math.byu.edu |
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Ji Li Department of Mathematics Michigan State University East Lansing, MI 48824, USA email: liji@math.msu.edu |
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Meir Shillor Department of Mathematics and Statistics Oakland University Rochester, MI 48309, USA email: shillor@oakland.edu |
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