A New Blow-Up Criterion to a Singular Non-Newton Polytropic Filtration Equation

Qingwei Li and Menglan Liao ()
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Qingwei Li: School of Science, Dalian Maritime University, Dalian 116026, China
Menglan Liao: College of Science, Hohai University, Nanjing 210098, China

Mathematics, 2023, vol. 11, issue 6, 1-8

Abstract: In this paper, a singular non-Newton polytropic filtration equation under the initial-boundary value condition is revisited. The finite time blow-up results were discussed when the initial energy E ( u 0 ) was subcritical ( E ( u 0 ) < d ), critical ( E ( u 0 ) = d ), and supercritical ( E ( u 0 ) > d ), with d being the potential depth by using the potential well method and some differential inequalities. The goal of this paper is to give a finite time blow-up result if E ( u 0 ) is independent of d . Moreover, the explicit upper bound of the blow-up time is obtained by the classical Levine’s concavity method, and the precise lower bound of the blow-up time is derived by applying an interpolation inequality.

Keywords: non-Newton polytropic filtration equation; blow-up; the upper and lower bounds of the blow-up time (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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