Quasilinear Parabolic Equations Associated with Semilinear Parabolic Equations-Reference-Cited by-同舟云学术

Quasilinear Parabolic Equations Associated with Semilinear Parabolic Equations

Published:2023-02-02 Issue:3 Volume:11 Page:758
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Ishii Katsuyuki¹^ORCID,Pierre Michel²,Suzuki Takashi³^ORCID

Affiliation:

1. Graduate School of Maritime Sciences, Kobe University, Kobe 658-0022, Japan

2. Department of Mathematics, École Normale Supérieure de Rennes, 35170 Bruz, France

3. 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.

Publisher

MDPI AG

Subject

General Medicine

Link

https://www.mdpi.com/2227-7390/11/3/758/pdf

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