Weak Comparison Principles for Fully Nonlinear Degenerate Parabolic Equations with Discontinuous Source Terms

被引：0

作者：

Hamamuki, Nao ^{[1
]}

Misu, Kuniyasu ^{[1
]}

机构：

[1] Hokkaido Univ, Fac Sci, Dept Math, Sapporo, Japan

来源：

MINIMAX THEORY AND ITS APPLICATIONS | 2023年 / 8卷 / 01期

关键词：

Weak comparison principle; viscosity solution; fully nonlinear equation; discontinuous source term; level-set mean curvature flow equation; VISCOSITY SOLUTIONS; ASYMPTOTIC SPEED; EXISTENCE; CRYSTALS; MOTION;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the initial value problem for a fully nonlinear degenerate parabolic equation with dis-continuous source terms, to which a usual type of comparison principles does not apply. Examples include singular equations appearing in surface evolution problems such as the level-set mean curva-ture flow equation with a driving force term and a discontinuous source term. By a suitable scaling, we establish weak comparison principles for a viscosity sub-and supersolution to the equation. We also present uniqueness and existence results of possibly discontinuous viscosity solutions.

引用

页码：37 / 60

页数：24

共 50 条

[21] Nonlinear degenerate parabolic equations with measure data
Li, FQ
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 61 (07) : 1269 - 1282
[22] Convergence Rates for Semi-Discrete Splitting Approximations for Degenerate Parabolic Equations with Source Terms
E. R. Jakobsen
K. H. Karlsen
BIT Numerical Mathematics, 2005, 45 : 37 - 67
[23] Nonlinear Degenerate Parabolic Equations with a Singular Nonlinearity
Khelifi, Hichem
Mokhtari, Fares
ACTA APPLICANDAE MATHEMATICAE, 2024, 189 (01)
[24] Convergence rates for semi-discrete splitting approximations for degenerate parabolic equations with source terms
Jakobsen, ER
Karlsen, KH
BIT NUMERICAL MATHEMATICS, 2005, 45 (01) : 37 - 67
[25] A splitting method for fully nonlinear degenerate parabolic PDEs
Tan, Xiaolu
ELECTRONIC JOURNAL OF PROBABILITY, 2013, 18 : 1 - 24
[26] New strong maximum and comparison principles for fully nonlinear degenerate elliptic PDEs
Bardi, Martino
Goffi, Alessandro
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2019, 58 (06)
[27] COMPARISON OF VISCOSITY SOLUTIONS OF FULLY NONLINEAR DEGENERATE PARABOLIC PATH-DEPENDENT PDEs
Ren, Zhenjie
Touzi, Nizar
Zhang, Jianfeng
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2017, 49 (05) : 4093 - 4116
[28] Weak Harnack inequality for fully nonlinear uniformly parabolic equations with unbounded ingredients and applications
Koike, Shigeaki
Swiech, Andrzej
Tateyama, Shota
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2019, 185 : 264 - 289
[29] Asymptotic behavior in degenerate parabolic fully nonlinear equations and its application to elliptic eigenvalue problems
Kim, Soojung
Lee, Ki-Ahm
JOURNAL OF DIFFERENTIAL EQUATIONS, 2013, 254 (08) : 3259 - 3306
[30] The blow-up phenomenon for degenerate parabolic equations with variable coefficients and nonlinear source
Cianci, P.
Martynenko, A. V.
Tedeev, A. F.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 73 (07) : 2310 - 2323

← 1 2 3 4 5 →