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Non-autonomous semilinear evolution equations with almost sectorial operators

Non-autonomous semilinear evolution equations with almost sectorial operators Inspired by the theory of semigroups of growth α, we construct an evolution process of growth α. The abstract theory is applied to study semilinear singular non-autonomous parabolic problems. We prove that, under natural assumptions, a reasonable concept of solution can be given to such semilinear singularly non-autonomous problems. Applications are considered to non-autonomous parabolic problems in space of Hölder continuous functions and to a parabolic problem in a domain $$\Omega \subset {\mathbb{R}}^n$$ with a one dimensional handle. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Evolution Equations Springer Journals

Non-autonomous semilinear evolution equations with almost sectorial operators

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References (16)

Publisher
Springer Journals
Copyright
Copyright © 2008 by Birkhaueser
Subject
Mathematics; Analysis
ISSN
1424-3199
eISSN
1424-3202
DOI
10.1007/s00028-008-0394-3
Publisher site
See Article on Publisher Site

Abstract

Inspired by the theory of semigroups of growth α, we construct an evolution process of growth α. The abstract theory is applied to study semilinear singular non-autonomous parabolic problems. We prove that, under natural assumptions, a reasonable concept of solution can be given to such semilinear singularly non-autonomous problems. Applications are considered to non-autonomous parabolic problems in space of Hölder continuous functions and to a parabolic problem in a domain $$\Omega \subset {\mathbb{R}}^n$$ with a one dimensional handle.

Journal

Journal of Evolution EquationsSpringer Journals

Published: Nov 1, 2008

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