Quasilinear Parabolic Equations Associated with Semilinear Parabolic Equations

被引：0

作者：

Ishii, Katsuyuki ^{[1
]}

Pierre, Michel ^{[2
]}

Suzuki, Takashi ^{[3
]}

机构：

[1] Kobe Univ, Grad Sch Maritime Sci, Kobe 6580022, Japan

[2] Ecole Normale Super Rennes, Dept Math, F-35170 Bruz, France

[3] Osaka Univ, Ctr Math Modeling & Data Sci, Osaka 5650871, Japan

来源：

MATHEMATICS | 2023年 / 11卷 / 03期

关键词：

semilinear parabolic equation; quasilinear parabolic equation; blowup pattern; COMPLETE BLOW-UP; SET;

D O I：

10.3390/math11030758

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：23

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