On some classes of coefficient inverse problems for parabolic systems of equations

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• 作者：S. G. Pyatkov (1) (2)
  M. L. Samkov (2)
  
• 关键词：inverse problem ; parabolic system ; boundary value problem ; overdetermination condition
• 刊名：Siberian Advances in Mathematics
• 出版年：2012
• 出版时间：October 2012
• 年：2012
• 卷：22
• 期：4
• 页码：287-302
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• 作者单位：S. G. Pyatkov (1) (2)
  M. L. Samkov (2)
  
  1. Ugra State University, Hanty-Mansi沫sk, 628012, Russia
  2. Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia
  
• ISSN：1934-8126

文摘

We examine the question on solvability in the Sobolev spaces of coefficient inverse problems for parabolic systems of equations with the overdetermination conditions on a collection of surfaces. Under certain conditions on the geometry of the domain and the boundary operators, the local solvability of the problem is proven. It is demonstrated that the conditions on the boundary operators are sharp and that, in some cases, the problem is not unconditionally solvable.