Piasecki, T;
Shibata, Y;
Zatorska, E;
(2020)
On the maximal Lp-Lq regularity of solutions to a general linear parabolic system.
Journal of Differential Equations
, 268
(7)
pp. 3332-229.
10.1016/j.jde.2019.09.058.
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Abstract
We show the existence of solution in the maximal regularity framework to a class of symmetric parabolic problems on a uniformly domain in . Our approach consist in showing - boundedness of families of solution operators to corresponding resolvent problems first in the whole space, then in half-space, perturbed half-space and finally, using localization arguments, on the domain. Assuming additionally boundedness of the domain we also show exponential decay of the solution. In particular, our approach does not require assuming a priori the uniform Lopatinskii - Shapiro condition.
| Type: | Article |
|---|---|
| Title: | On the maximal Lp-Lq regularity of solutions to a general linear parabolic system |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.jde.2019.09.058 |
| Publisher version: | https://doi.org/10.1016/j.jde.2019.09.058 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | linear parabolic system, maximal regularity, R-boundedness |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10085459 |
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