Pseudo $ S $-asymptotically Bloch type periodic solutions to a damped evolution equation

Siqi Chen; Yong-Kui Chang; Yanyan Wei

doi:10.3934/eect.2021017

Article Contents

2022, Volume 11, Issue 3: 621-633. Doi: 10.3934/eect.2021017

This issue Previous Article Next Article Initial boundary value problem for a strongly damped wave equation with a general nonlinearity

Pseudo $ S $-asymptotically Bloch type periodic solutions to a damped evolution equation

School of Mathematics and Statistics, Xidian University, Xi'an 710071, Shaanxi, China

^* Corresponding author: Yong-Kui Chang
^* Corresponding author: Yong-Kui Chang

Received: August 31, 2020

Revised: January 31, 2021

Published: June 2022

This work is partially supported by NSF of Shaanxi Province (2020JM-183)

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Abstract

This paper is mainly concerned with the existence of pseudo S-asymptotically Bloch type periodic solutions to damped evolution equations in Banach spaces. Some existence results for classical Cauchy conditions and nonlocal Cauchy conditions are established through properties of pseudo S-asymptotically Bloch type periodic functions and regularized families. The obtained results show that for each pseudo S-asymptotically Bloch type periodic input forcing disturbance, the output mild solutions to reference equations remain pseudo S-asymptotically Bloch type periodic.

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Mathematics Subject Classification: Primary: 34K13, 58D25; Secondary: 34C25.

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