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Global Solutions and Blow-Up for the Wave Equation with Variable Coefficients: I. Interior Supercritical Source

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Abstract

In this paper, we consider the variable coefficient wave equation with damping and supercritical source terms. The goal of this work is devoted to prove the local and global existence, and classify decay rate of energy depending on the growth near zero on the damping term. Moreover, we prove the blow-up of the weak solution with positive initial energy as well as nonpositive initial energy.

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Acknowledgements

This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education (NRF-2019R1I1A3A01051714).

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  1. Department of Mathematics, and Institute of Pure and Applied Mathematics, Jeonbuk National University, Jeonju, 54896, Republic of Korea

    Tae Gab Ha

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Ha, T.G. Global Solutions and Blow-Up for the Wave Equation with Variable Coefficients: I. Interior Supercritical Source. Appl Math Optim 84 (Suppl 1), 767–803 (2021). https://doi.org/10.1007/s00245-021-09785-5

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