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Infinite Time Blow-Up of Solutions for A Class of Logarithmic Wave Equations with Arbitrary High Initial Energy

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Abstract

This paper deals with a class of logarithmic wave equations from physics. By developing a completely different method from the previous studies, we prove for the first time how to extend the maximal existence time of solutions to infinity, which can be generalized to most kinds of logarithmic wave equations; then we prove that the solutions will blow up at infinite time with arbitrary high initial energy. The results of this paper give an answer to the open problem of a recent paper (Appl Math Optim 79(1):131–144 (2019)).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, People’s Republic of China

    Hang Ding & Jun Zhou

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  1. Hang Ding
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  2. Jun Zhou
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Correspondence to Jun Zhou.

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Ding, H., Zhou, J. Infinite Time Blow-Up of Solutions for A Class of Logarithmic Wave Equations with Arbitrary High Initial Energy. Appl Math Optim 84 (Suppl 2), 1331–1343 (2021). https://doi.org/10.1007/s00245-021-09797-1

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  • DOI: https://doi.org/10.1007/s00245-021-09797-1

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