Existence of Viscosity Solutions for Weakly Coupled Cooperative Parabolic Systems with Fully Nonlinear Principle Part

被引：0

作者：

Boyadzhiev, Georgi ^{[1
,2
]}

Kutev, Nikolay ^{[1
]}

机构：

[1] Bulgarian Acad Sci, Inst Math & Informat, 8 Acad G Bonchev St, Sofia 1113, Bulgaria

[2] Univ Architecture Civil Engn & Geodesy, 1 Hr Smirnenski Bul, Sofia 1046, Bulgaria

来源：

MATHEMATICS | 2024年 / 12卷 / 13期

关键词：

degenerate parabolic quasi-monotone systems; viscosity solutions; maximum principle; existence; STRONG MAXIMUM PRINCIPLE; EQUATIONS;

D O I：

10.3390/math12132093

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, the existence of viscosity solutions for weakly coupled, degenerate, and cooperative parabolic systems is studied in a bounded domain. In particular, we consider the viscosity solutions of parabolic systems with fully nonlinear degenerated principal symbol and linear coupling part. The maximum principle theorem is given as well.

引用

页数：10

共 50 条

[21] MAXIMUM PRINCIPLE AND EXISTENCE OF POSITIVE SOLUTIONS FOR NONLINEAR SYSTEMS ON RN [J].

Serag, Hassan M. ;

El-Zahrani, Eada A. .

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2005,

[22] COMPARISON OF VISCOSITY SOLUTIONS OF FULLY NONLINEAR DEGENERATE PARABOLIC PATH-DEPENDENT PDEs [J].

Ren, Zhenjie ;

Touzi, Nizar ;

Zhang, Jianfeng .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2017, 49 (05) :4093-4116

[23] On existence and uniqueness of viscosity solutions for second order fully nonlinear PDEs with Caputo time fractional derivatives [J].

Namba, Tokinaga .

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2018, 25 (03)

[24] Asymptotic behavior of solutions to a class of coupled nonlinear parabolic systems [J].

Leng, Yan ;

Nie, Yuanyuan ;

Zhou, Qian .

BOUNDARY VALUE PROBLEMS, 2019, 2019 (1)

[25] The Phragmen-Lindelof theorem for Lp-viscosity solutions of fully nonlinear parabolic equations with unbounded ingredients [J].

Tateyama, Shota .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2020, 133 :172-184

[26] ON THE STRONG MAXIMUM PRINCIPLE FOR FULLY NONLINEAR PARABOLIC EQUATIONS OF SECOND ORDER [J].

Goffi, Alessandro .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2025, 153 (04) :1575-1583

[27] Fujita type exponent for fully nonlinear parabolic equations and existence results [J].

Meneses, Rodrigo ;

Quaas, Alexander .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 376 (02) :514-527

[28] Existence and uniqueness of viscosity solutions for parabolic Hessian equations [J].

Guo, Xuewen ;

Zhao, Huawei .

2ND INTERNATIONAL CONFERENCE ON APPLIED MATHEMATICS, MODELLING, AND INTELLIGENT COMPUTING (CAMMIC 2022), 2022, 12259

[29] The existence of minimal large positive solutions for a class of nonlinear cooperative systems [J].

Lopez-Gomez, Julian ;

Maire, Luis .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2022, 68

[30] Existence, uniqueness and behavior of solutions for a class of nonlinear parabolic problems [J].

Porzio, Maria Michaela .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (16) :5359-5382

← 1 2 3 4 5 →