BOUNDARY VALUE AND EXTREMAL PROBLEMS FOR THE NONLINEAR CONVECTION - DIFFUSION - REACTION EQUATION

被引：11

作者：

Brizitskii, R., V ^{[1
,2
]}

Saritskaya, Zh. Yu ^{[2
]}

机构：

[1] Inst Appl Math FEB RAS, Str Radio 7, Vladivostok 690041, Russia

[2] Far Earstern Fed Univ, Vladivostok 690000, Russia

来源：

SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA | 2015年 / 12卷

关键词：

convection-diffusion-reaction equation; control problem; optimality system; local uniqueness;

D O I：

10.17377/semi.2015.12.038

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the boundary value and optimal control problems for stationary nonlinear convection-diffusion-reaction equation, wherein reaction coefficient depends on concentration of substance. The general form of nonlinear reaction coefficient's dependence on concentration of substance is offered. Solvability of the boundary value and control problems for convection-diffusion-reaction equation is proved. Nonlocal optimality system for the quadratic nonlinearity is obtained, and local uniqueness of extremal problem's solution for a particular cost functional is proved with the help of optimality system.

引用

页码：447 / 456

页数：10

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