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Quasilinear Parabolic Equations Associated with Semilinear Parabolic Equations

Author

Listed:
  • Katsuyuki Ishii

    (Graduate School of Maritime Sciences, Kobe University, Kobe 658-0022, Japan)

  • Michel Pierre

    (Department of Mathematics, École Normale Supérieure de Rennes, 35170 Bruz, France)

  • Takashi Suzuki

    (Center for Mathematical Modeling and Data Science, Osaka University, Osaka 565-0871, Japan)

Abstract

We formulate a quasilinear parabolic equation describing the behavior of the global-in-time solution to a semilinear parabolic equation. We study this equation in accordance with the blow-up and quenching patterns of the solution to the original semilinear parabolic equation. This quasilinear equation is new in the theory of partial differential equations and presents several difficulties for mathematical analysis. Two approaches are examined: functional analysis and a viscosity solution.

Suggested Citation

  • Katsuyuki Ishii & Michel Pierre & Takashi Suzuki, 2023. "Quasilinear Parabolic Equations Associated with Semilinear Parabolic Equations," Mathematics, MDPI, vol. 11(3), pages 1-23, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:758-:d:1055418
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