Taiwanese Journal of Mathematics

Almost Periodicity of All $L^2$-bounded Solutions of a Functional Heat Equation

Qi-Ru Wang and Zhi-Qiang Zhu

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Abstract

In this paper, we continue the investigations done in the literature about the so called Bohr-Neugebauer property for almost periodic differential equations. More specifically, for a class of functional heat equations, we prove that each $L^2$-bounded solution is almost periodic. This extends a result in [5] to the delay case.

Article information

Source
Taiwanese J. Math., Advance publication (2019), 7 pages.

Dates
First available in Project Euclid: 29 May 2019

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1559095225

Digital Object Identifier
doi:10.11650/tjm/190506

Subjects
Primary: 35K05: Heat equation 35B15: Almost and pseudo-almost periodic solutions

Keywords
functional heat equations Poincaré inequality Hölder inequality almost periodic solutions

Citation

Wang, Qi-Ru; Zhu, Zhi-Qiang. Almost Periodicity of All $L^2$-bounded Solutions of a Functional Heat Equation. Taiwanese J. Math., advance publication, 29 May 2019. doi:10.11650/tjm/190506. https://projecteuclid.org/euclid.twjm/1559095225


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