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IPM
30
YEARS OLD

“School of Mathematics”

Paper   IPM / M / 2329
   School of Mathematics
  Title: Determination of an unknown coefficient in a parabolic inverse problem
  Author(s):
1 . H. Azari
2 . Ch. Li
3 . Y. Nie
4 . Sh. Zhang
  Status: Published
  Journal: Dynam. Contin. Discrete Impuls. Systems
  Vol.: 11
  Year: 2004
  Pages: 665-674
  Supported by: IPM
  Abstract:
In this paper we study a parabolic inverse problem of finding a(t) such that ut = a(t) uxx subject to initial-boundary value conditions and an over-specified condition. We use the over-specified information to solve for the unknown function and then transform these inverse problems into some nonclassical equations in which a trace type of functional is involved. By applying the maximum principle, we deduce some a priori estimates for the solution of our nonclassical problem. Then the continuity methods can be applied to establish the global existences of solutions to these problems.

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