Abstract

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 Fréchet differentiable.

中文翻译：

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非线性反应-扩散-对流方程的边值和极值问题分析

摘要

在方程中的反应系数和边界条件中的传质系数非线性地依赖于物质浓度的情况下，证明了反应-扩散-对流方程边值问题的全局可解性。建立了浓度的最小和最大原则。乘法控制问题的可解性得到了一般形式的证明。在模型的性能泛函和解相关系数是 Fréchet 可微的假设下，推导了最优系统，并为极值问题建立了 bang-bang 原理。