TY  - JOUR
AV  - public
Y1  - 2020/03/15/
EP  - 229
TI  - On the maximal Lp-Lq regularity of solutions to a general linear parabolic system
N2  - 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.
ID  - discovery10085459
KW  - linear parabolic system
KW  -  maximal regularity
KW  -  R-boundedness
VL  - 268
SP  - 3332
IS  - 7
N1  - This version is the author accepted manuscript. For information on re-use, please refer to the publisher?s terms and conditions.
UR  - https://doi.org/10.1016/j.jde.2019.09.058
SN  - 1090-2732
A1  - Piasecki, T
A1  - Shibata, Y
A1  - Zatorska, E
JF  - Journal of Differential Equations
ER  -