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

Yanjin Wang () and Jianzhen Qian
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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

Mathematics, 2022, vol. 10, issue 16, 1-9

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.

Keywords: parabolic equation; exponential nonlinearity; blow-up (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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