Abstract
We introduce a method for showing a priori Lp estimates for time-periodic, linear, partial differential equations set in a variety of domains such as the whole space, the half space and bounded domains. The method is generic and can be applied to a wide range of problems. We demonstrate it on the heat equation. The main idea is to replace the time axis with a torus in order to reformulate the problem on a locally compact abelian group and to employ Fourier analysis on this group. As a by-product, maximal Lp regularity for the corresponding initial-value problem follows without the notion of R-boundedness. Moreover, we introduce the concept of a time-periodic fundamental solution.
Original language | English |
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Pages (from-to) | 633-652 |
Number of pages | 20 |
Journal | Journal of Differential Equations |
Volume | 262 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2017 Jan 5 |
Externally published | Yes |
Keywords
- A priori estimates
- Heat equation
- Maximal regularity
- Time-periodic
ASJC Scopus subject areas
- Analysis
- Applied Mathematics