Analysis of Boundary Value and Extremum Problems for a Nonlinear Reaction-Diffusion-Convection Equation

被引：9

作者：

Brizitskii, R., V ^{[1
]}

Bystrova, V. S. ^{[2
]}

Saritskaia, Zh Yu ^{[1
]}

机构：

[1] Russian Acad Sci, Inst Appl Math, Far East Branch, Vladivostok 690041, Russia

[2] Far Eastern Fed Univ, Vladivostok 690090, Russia

来源：

DIFFERENTIAL EQUATIONS | 2021年 / 57卷 / 05期

关键词：

THERMAL CLOAKING; STABILITY;

D O I：

10.1134/S0012266121050062

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The global solvability of boundary value problems for the reaction-diffusion-convection equation is proved for the case in which the reaction coefficient in the equation and the mass transfer coefficient in the boundary condition nonlinearly depend on the substance concentration. The minimum and maximum principle for the concentration is established. The solvability of multiplicative control problems is proved in general form. Optimality systems are derived and the presence of the bang-bang principle is established for extremum problems under the assumption that the performance functionals and the solution-dependent coefficients of the model are Frechet differentiable.

引用

页码：615 / 629

页数：15

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