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Parabolic Finslerian Allen–Cahn equation and its Harnack inequality

Bin Shen

https://orcid.org/0000-0001-9505-9029

School of Mathematics, Southeast University, Dongnandaxue Road 2, Nanjing 211189, Jiangsu, P. R. China

E-mail Address: shenbin@seu.edu.cn

Corresponding author.

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and

Hao Zhang

School of Mathematics, Southeast University, Dongnandaxue Road 2, Nanjing 211189, Jiangsu, P. R. China

E-mail Address: 213210007@seu.edu.cn

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https://doi.org/10.1142/S0129167X24500587Cited by:0 (Source: Crossref)

Abstract

Parabolic Finslerian Allen–Cahn equation is a quasilinear parabolic equation on Finsler metric measure spaces. In this paper, we establish a Harnack inequality for solutions to this equation on compact Finsler metric measure spaces using geometric methods. Moreover, we give a degree 4 polynomial gradient estimate of the traveling wave solution on flat-curved spaces.

Communicated by Yuguang Shi

Keywords:

AMSC: 35K55, 53C60, 58J35

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