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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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.

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

First available in Project Euclid: 22 April 2020

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

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


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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