Decay of C0-semigroups and local decay of waves on even (and odd) dimensional exterior domains View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2018-12

AUTHORS

Reinhard Stahn

ABSTRACT

We prove decay rates for a vector-valued function f of a nonnegative real variable with bounded weak derivative, under rather general conditions on the Laplace transform f^. This generalizes results of Batty and Duyckaerts (J Evol Equ 8(4):765–780, 2008) and other authors in later publications. Besides the possibility of f^ having a singularity of logarithmic type at zero, one novelty in our paper is that we assume f^ to extend to a domain to the left of the imaginary axis, depending on a nondecreasing function M and satisfying a growth assumption with respect to a different nondecreasing function K. The decay rate is expressed in terms of M and K. We prove that the obtained decay rates are essentially optimal for a very large class of functions M and K. Finally, we explain in detail how our main result improves known decay rates for the local energy of waves on exterior domains. More... »

PAGES

1-42

Journal

TITLE

Journal of Evolution Equations

ISSUE

N/A

VOLUME

N/A

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00028-018-0455-1

DOI

http://dx.doi.org/10.1007/s00028-018-0455-1

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1104262461


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