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 -