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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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

Taiwanese J. Math., Volume 24, Number 2 (2020), 413-419.

Received: 13 September 2018
Revised: 16 March 2019
Accepted: 23 May 2019
First available in Project Euclid: 29 May 2019

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Zentralblatt MATH identifier

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

functional heat equations Poincaré inequality Hölder inequality almost periodic solutions


Wang, Qi-Ru; Zhu, Zhi-Qiang. Almost Periodicity of All $L^2$-bounded Solutions of a Functional Heat Equation. Taiwanese J. Math. 24 (2020), no. 2, 413--419. doi:10.11650/tjm/190506. https://projecteuclid.org/euclid.twjm/1559095225

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