On solvability of inverse coefficient problems for nonlinear convection—diffusion—reaction equation

All-Russian conference on Nonlinear Waves: Theory and New Applications

Brizitskii, R.V.^1,2 ; Saritskaya, Zh.Yu.^2

Institute of Applied Mathematics FEB RAS, Vladivostok, Russia^1

Far Eastern Federal University, Vladivostok, Russia^2

关键词: Existence of Solutions;    Inverse coefficient problem;    Nonlinear boundary value problems;    Nonlinear convection;    Spatial variables;    Substance concentrations;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/722/1/012007/pdf
DOI  :  10.1088/1742-6596/722/1/012007

来源: IOP

【 摘 要 】

An inverse coefficient problem is considered for a stationary nonlinear convection- diffusion-reaction equation, in which reaction coefficient has a rather common dependence on substance concentration and on spacial variable. The solvability of the considered nonlinear boundary value problem is proved in a general case. The existence of solutions of the inverse problem is proved for the reaction coefficients, which are defined by the product of two functions. The first function depends on a spatial variable, the second one depends nonlinearly on the solution of the boundary value problem. The mentioned inverse problem consists in reconstructing the first function with the help of additional information provided by the solution of the boundary value problem.