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A gradient maximum principle of solutions for a quasilinear parabolic equation

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Abstract

This short note is concerned with a quasilinear diffusion equation under initial and Neumann boundary value condition. To be more precise, the authors establish a gradient maximum principle of classical solutions via the maximum principle and Hopf’s lemma. The result generalizes a recent work obtained by Kim (Proc Amer Math Soc 145:1203–1208, 2017).

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Acknowledgements

The authors wish to express their sincere gratitude to Professor Wenjie Gao for his support and constant encouragement. The second author would like to thank Professor Baisheng Yan for his critical guidance during the visit to Michigan State University.

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Authors and Affiliations

  1. College of Science, Dalian Maritime University, Dalian, 116026, Liaoning Province, China

    Qingwei Li

  2. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, Fujian, China

    Menglan Liao

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  1. Qingwei Li
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  2. Menglan Liao
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Correspondence to Menglan Liao.

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Li, Q., Liao, M. A gradient maximum principle of solutions for a quasilinear parabolic equation. Arch. Math. 116, 677–682 (2021). https://doi.org/10.1007/s00013-021-01582-4

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  • DOI: https://doi.org/10.1007/s00013-021-01582-4

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