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J. Korean Math. Soc. 2021; 58(6): 1433-1448

Online first article August 2, 2021      Printed November 1, 2021

https://doi.org/10.4134/JKMS.j210084

Copyright © The Korean Mathematical Society.

Existence and general decay for a viscoelastic equation with logarithmic nonlinearity

Tae Gab Ha, Sun-Hye Park

Jeonbuk National University; Pusan National University

Abstract

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In the present work, we investigate a viscoelastic equation involving a logarithmic nonlinear source term. After proving the existence of solutions, we establish a general decay estimate of the solution using energy estimates and theory of convex functions. This result extends and complements some previous results of \cite{ha-par, mus}.

Keywords: General decay, logarithmic source, viscoelastic equation, convex function

MSC numbers: 35L70, 35B40, 35L05, 35B35

Supported by: The first author was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education (NRF-2019R1I1A3A01051714). The second author was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education (2020R1I1A3066250).

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