Inverse Problems with Pointwise Overdetermination for some Quasilinear Parabolic Systems

被引：0
作者：
Pyatkov S.G. [1 ,2 ]
Rotko V.V. [1 ]
机构：
[1] Yugra State University, Khanty-Mansiisk
[2] Sobolev Institute of Mathematics, Novosibirsk
来源：
Siberian Advances in Mathematics | 2020年 / 30卷 / 2期
基金：
俄罗斯基础研究基金会;
关键词：
convection-diffusion; heat-and-mass transfer; inverse problem; parabolic system; source function;
D O I：
10.3103/S1055134420020054
中图分类号：
学科分类号：
摘要：
Abstract: In the article, we examine well-posedness questions in the Sobolev spaces of the inversesource problem in the case of a quasilinear parabolic system of the second order. The main part ofthe operator is linear. The overdetermination conditions are values of a solution at some collectionof interior points. It is demonstrated that, in the case of at most linear growth of the nonlinearity,there exists a unique global (in time) solution and the problem is well-posed in the Sobolevclasses. The conditions on the data are minimal and the results are sharp. © 2020, Allerton Press, Inc.
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页码：124 / 142
页数：18
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