Rocky Mountain Journal of Mathematics

A new blow-up criterion for non-Newton filtration equations with special medium void

Yuzhu Han

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Abstract

This paper deals with the finite time blow-up of solutions to the initial boundary value problem of a non-Newton filtration equation with special medium void. A new criterion for the solutions to blow up in finite time is established by using the Hardy inequality. Moreover, the upper and lower bounds for the blow-up time are also estimated. The results solve an open problem proposed by Liu in 2016.

Article information

Source
Rocky Mountain J. Math., Volume 48, Number 8 (2018), 2489-2501.

Dates
First available in Project Euclid: 30 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1546138818

Digital Object Identifier
doi:10.1216/RMJ-2018-48-8-2489

Mathematical Reviews number (MathSciNet)
MR3894990

Zentralblatt MATH identifier
1403.35122

Subjects
Primary: 35K20: Initial-boundary value problems for second-order parabolic equations 35K59: Quasilinear parabolic equations

Keywords
Non-Newton filtration equation medium void blow-up criterion Hardy inequality

Citation

Han, Yuzhu. A new blow-up criterion for non-Newton filtration equations with special medium void. Rocky Mountain J. Math. 48 (2018), no. 8, 2489--2501. doi:10.1216/RMJ-2018-48-8-2489. https://projecteuclid.org/euclid.rmjm/1546138818


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