Small data blow-up of semi-linear wave equation with scattering dissipation and time-dependent mass

Masahiro Ikeda; Ziheng Tu; Kyouhei Wakasa

doi:10.3934/eect.2021011

Article Contents

2022, Volume 11, Issue 2: 515-536. Doi: 10.3934/eect.2021011

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Small data blow-up of semi-linear wave equation with scattering dissipation and time-dependent mass

1.
Department of Mathematics, Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, 223-8522, Japan, Center for Advanced Intelligence Project, RIKEN, Japan
2.
Department of Mathematics, School of Data Science, Zhejiang University of Finance and Economics, 310018, Hangzhou, P.R.China
3.
Department of Creative Engineering, National Institute of Technology, Kushiro College, 2-32-1 Otanoshike-Nishi, Kushiro-Shi, Hokkaido 084-0916, Japan

^* Corresponding author: Ziheng Tu
^* Corresponding author: Ziheng Tu

Received: March 2020

Revised: December 2020

Early access: March 2021

Published: April 2022

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Abstract

In the present paper, we study small data blow-up of the semi-linear wave equation with a scattering dissipation term and a time-dependent mass term from the aspect of wave-like behavior. The Strauss type critical exponent is determined and blow-up results are obtained to both sub-critical and critical cases with corresponding upper bound lifespan estimates. For the sub-critical case, our argument does not rely on the sign condition of dissipation and mass, which gives the extension of the result in [14]. Moreover, we show the blow-up result for the critical case which is a new result.

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Mathematics Subject Classification: Primary: 35L71; Secondary: 35B44.

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