The maximum and comparison principles for a system of two equations

被引:0
作者
Portnyagin, D. V. [1 ]
机构
[1] Inst Condensed Matter Phys, Lvov, Ukraine
关键词
nondiagonal parabolic system; nondiagonal elliptic system; maximum principle; comparison principle;
D O I
10.1134/S0037446612020115
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We propose a method of generalizing the well-known maximum and comparison principles to nondiagonal parabolic systems of second order nonlinear differential equations. Under consideration are the cases of Dirichlet and Neumann problems. We also present some examples of the systems that this method applies to.
引用
收藏
页码:291 / 300
页数:10
相关论文
共 50 条
[41]   Two maximum principles for a nonlinear fourth order equation from thin plate theory [J].
Danet, Cristian-Paul .
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2014, (31) :1-9
[42]   Maximum Principles for Second-Order Impulsive Integro-Differential Equations with Integral Jump Conditions [J].
Chatthai Thaiprayoon ;
Jessada Tariboon .
Bulletin of the Malaysian Mathematical Sciences Society, 2016, 39 :971-992
[43]   Local radial basis function collocation method preserving maximum and monotonicity principles for nonlinear differential equations [J].
Zheng, Zhoushun ;
He, Jilong ;
Du, Changfa ;
Ye, Zhijian .
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2023, 39 (05) :3964-3986
[44]   Maximum Principles for Second-Order Impulsive Integro-Differential Equations with Integral Jump Conditions [J].
Thaiprayoon, Chatthai ;
Tariboon, Jessada .
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2016, 39 (03) :971-992
[45]   Maximum principles and aleksandrov-bakelman-pucci type estimates for nonlocal schrodinger equations with exterior conditions [J].
Biswas, Anup ;
Lorinczi, Jozsef .
SIAM Journal on Mathematical Analysis, 2019, 51 (04) :1543-1581
[46]   Random differential inequalities and comparison principles for nonlinear hybrid random differential equations [J].
Dhage, Bapurao C. ;
Metkar, Ram G. .
INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, 2015, 6 (02) :1-19
[47]   Comparison principles of fractional differential equations with non-local derivative and their applications [J].
Al-Refai, Mohammed ;
Baleanu, Dumitru .
AIMS MATHEMATICS, 2021, 6 (02) :1443-1451
[48]   Maximum Principle and Application of Parabolic Partial Differential Equations [J].
Dong Fangliang .
2012 INTERNATIONAL CONFERENCE ON MECHANICAL AND ELECTRONICS ENGINEERING, 2012, 3 :198-205
[49]   Maximum, anti-maximum principles and monotone methods for boundary value problems for Riemann-Liouville fractional differential equations in neighborhoods of simple eigenvalues [J].
Eloe, Paul W. ;
Neugebauer, Jeffrey T. .
CUBO-A MATHEMATICAL JOURNAL, 2023, 25 (02) :251-272
[50]   Nonlocal maximum principles for active scalars [J].
Kiselev, Alexander .
ADVANCES IN MATHEMATICS, 2011, 227 (05) :1806-1826