BOUNDARY CONTROL PROBLEM FOR THE REACTION-ADVECTION-DIFFUSION EQUATION WITH A MODULUS DISCONTINUITY OF ADVECTION

被引：1

作者：

Bulatov, P. E. ^{[1
,2
]}

Cheng, Han ^{[1
]}

Wei, Yuxuan ^{[1
]}

Volkov, V. T. ^{[1
]}

Levashova, N. T. ^{[1
]}

机构：

[1] Lomonosov Moscow State Univ, Fac Phys, Moscow, Russia

[2] Russian Acad Sci, Keldysh Inst Appl Math, Moscow, Russia

来源：

THEORETICAL AND MATHEMATICAL PHYSICS | 2024年 / 220卷 / 01期

基金：

俄罗斯科学基金会;

关键词：

Burgers equation; boundary control; asymptotic methods; small parameter; modulus nonlinearity; adaptive meshes; difference approximation; ASYMPTOTIC SOLUTION;

D O I：

10.1134/S0040577924070043

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We consider a periodic problem for a singularly perturbed parabolic reaction-diffusion-advection equation of the Burgers type with the modulus advection; it has a solution in the form of a moving front. We formulate conditions for the existence of such a solution and construct its asymptotic approximation. We pose a control problem where the required front propagation law is implemented by a specially chosen boundary condition. We construct an asymptotic solution of the boundary control problem. Using the asymptotic method of differential inequalities, we estimate the accuracy of the solution of the control problem. We propose an original numerical algorithm for solving singularly perturbed problems involving the modulus advection.

引用

页码：1097 / 1109

页数：13

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