Taiwanese Journal of Mathematics

Uniform Boundedness and Global Existence of Solutions to a Quasilinear Diffusion Equation with Nonlocal Fisher-KPP Type Reaction Term

Xueyan Tao and Zhong Bo Fang

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Abstract

This paper deals with the Cauchy problem and Neumann initial boundary value problem for a quasilinear diffusion equation with nonlocal Fisher-KPP type reaction terms. We establish the uniform boundedness and global existence of solutions to the problems by using multipliers technique and modified Moser's iteration argument for some ranges of parameters. Moreover, the ranges of parameters have similar structure to that of the classical critical Fujita exponent.

Article information

Source
Taiwanese J. Math., Advance publication (2020), 17 pages.

Dates
First available in Project Euclid: 22 April 2020

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1587520827

Digital Object Identifier
doi:10.11650/tjm/200402

Subjects
Primary: 35A01: Existence problems: global existence, local existence, non-existence 35B33: Critical exponents 35K59: Quasilinear parabolic equations

Keywords
quasilinear diffusion equation nonlocal Fisher-KPP reaction uniform boundedness global existence

Citation

Tao, Xueyan; Fang, Zhong Bo. Uniform Boundedness and Global Existence of Solutions to a Quasilinear Diffusion Equation with Nonlocal Fisher-KPP Type Reaction Term. Taiwanese J. Math., advance publication, 22 April 2020. doi:10.11650/tjm/200402. https://projecteuclid.org/euclid.twjm/1587520827


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