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Zbl 1059.35161
Azari, Houssin; Li, Changjun; Nie, Yiyong; Zhang, Shuhua
Determination of an unknown coefficient in a parabolic inverse problem. (English)
[J] Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 11, No. 5-6, 665-674 (2004). ISSN 1201-3390; ISSN 1918-2538/e

Summary: We study a parabolic inverse problem of finding $a(t)$ such that $u_t=a(t)u_{xx}$ 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 method can be applied to establish the global existences of solutions to these problems.

MSC 2000:: *35R30 Inverse problems for PDE
65M32 Inverse problems
35K05 Heat equation

Keywords: convergence; maximum principle; global existences

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