J. Evol. Equ. 18 (2018), 1633–1674 © 2018 Springer International Publishing AG, part of Springer Nature Journal of Evolution 1424-3199/18/041633-42, published online May 28, 2018 Equations https://doi.org/10.1007/s00028-018-0455-1 Decay of C -semigroups and local decay of waves on even (and odd) dimensional exterior domains 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
Journal of Evolution Equations – Springer Journals
Published: May 28, 2018
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.
Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.
All the latest content is available, no embargo periods.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera