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Blow-Up Time of Solutions for a Parabolic Equation with Exponential Nonlinearity

Author

Listed:
  • Yanjin Wang

    (Institute of Applied Physics and Computational Mathematics, No. 2, Fenghao-donglu, District Haidian, Beijing 100094, China)

  • Jianzhen Qian

    (Institute of Applied Physics and Computational Mathematics, No. 2, Fenghao-donglu, District Haidian, Beijing 100094, China)

Abstract

This paper studies a parabolic equation with exponential nonlinearity, which has several applications, for example the self-trapped beams in plasma. Based on a modified concavity method we prove the blow-up of the solution for initial data with high initial energy. We also proposed the solution’s lower and upper bound of the blow-up time for the equation. Our results complement the existing results.

Suggested Citation

  • Yanjin Wang & Jianzhen Qian, 2022. "Blow-Up Time of Solutions for a Parabolic Equation with Exponential Nonlinearity," Mathematics, MDPI, vol. 10(16), pages 1-9, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:16:p:2887-:d:886484
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