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

Author

Listed:
  • Qingwei Li

    (School of Science, Dalian Maritime University, Dalian 116026, China
    These authors contributed equally to this work.)

  • Menglan Liao

    (College of Science, Hohai University, Nanjing 210098, China
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Qingwei Li & Menglan Liao, 2023. "A New Blow-Up Criterion to a Singular Non-Newton Polytropic Filtration Equation," Mathematics, MDPI, vol. 11(6), pages 1-8, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1352-:d:1093545
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