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

[1] Strong Maximum Principle for Viscosity Solutions of Fully Nonlinear Cooperative Elliptic Systems
Boyadzhiev, Georgi
Kutev, Nikolai
MATHEMATICS, 2021, 9 (22)
[2] Viscosity solutions of fully nonlinear parabolic systems
Liu, WI
Yang, Y
Lu, G
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2003, 281 (01) : 362 - 381
[3] Remarks on the strong maximum principle for viscosity solutions to fully nonlinear parabolic equations
Da Lio, F
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2004, 3 (03) : 395 - 415
[4] ON UNIQUENESS AND EXISTENCE OF ENTROPY SOLUTIONS OF WEAKLY COUPLED SYSTEMS OF NONLINEAR DEGENERATE PARABOLIC EQUATIONS
Holden, Helge
Karlsen, Kenneth H.
Risebro, Nils H.
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2003,
[5] VISCOSITY SOLUTIONS OF FULLY NONLINEAR PARABOLIC PATH DEPENDENT PDES: PART II
Ekren, Ibrahim
Touzi, Nizar
Zhang, Jianfeng
ANNALS OF PROBABILITY, 2016, 44 (04) : 2507 - 2553
[6] Weakly coupled systems of fully nonlinear parabolic equations in the Heisenberg group
Liu, Qing
Zhou, Xiaodan
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2018, 174 : 54 - 78
[7] VISCOSITY SOLUTIONS OF FULLY NONLINEAR PARABOLIC PATH DEPENDENT PDES: PART I
Ekren, Ibrahim
Touzi, Nizar
Zhang, Jianfeng
ANNALS OF PROBABILITY, 2016, 44 (02) : 1212 - 1253
[8] Symmetry of viscosity solutions for fully nonlinear parabolic equations
Dai, Limei
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2016, 29 : 68 - 79
[9] Parabolic Minkowski convolutions and concavity properties of viscosity solutions to fully nonlinear equations
Ishige, Kazuhiro
Liu, Qing
Salani, Paolo
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2020, 141 : 342 - 370
[10] ON THE MAXIMUM PRINCIPLE FOR VISCOSITY SOLUTIONS OF FULLY NONLINEAR ELLIPTIC EQUATIONS IN GENERAL DOMAINS
Dolcetta, I. Capuzzo
Vitolo, A.
MATEMATICHE, 2007, 62 (02): : 69 - 91

← 1 2 3 4 5 →