On the maximal Lp-Lq regularity of solutions to a general linear parabolic system

Tomasz Piasecki, Yoshihiro Shibata, Ewelina Zatorska

研究成果: Article

抄録

We show the existence of solution in the maximal Lp−Lq regularity framework to a class of symmetric parabolic problems on a uniformly C2 domain in Rn. Our approach consist in showing R - 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.

元の言語English
ジャーナルJournal of Differential Equations
DOI
出版物ステータスAccepted/In press - 2019 1 1

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Regularity of Solutions
Parabolic Systems
Linear Systems
Half-space
R-boundedness
Maximal Regularity
Parabolic Problems
Exponential Decay
Resolvent
Existence of Solutions
Boundedness
Operator

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

これを引用

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AB - We show the existence of solution in the maximal Lp−Lq regularity framework to a class of symmetric parabolic problems on a uniformly C2 domain in Rn. Our approach consist in showing R - 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.

KW - Linear parabolic system

KW - Maximal regularity

KW - R-boundedness

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