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Determination of source parameter in parabolic equations. (English) Zbl 0767.35105

The authors prove uniqueness and existence of a function \(p(t)\) entering the semilinear parabolic equation \(u_ t=Lu+p(t)u+F(x,t,u,\nabla u,p(t))\) from the initial data, the lateral Dirichlet data, and either a weighted integral of \(u\) over certain domain in \(x\)-space or \(u(y,t)\) for some fixed \(y\) and all times \(t\) considered. Here \(L\) is a general second order elliptic operator. They assume that \(F\) is of no more than linear growth in \(u\) and \(p\) and in fact bounded in \(\nabla u\). Results of numerical experiments are given.
Recently the reviewer obtained global uniqueness results for all terms \(F(x,t,u)\) [Arch. Ration. Mech. Anal. (1993; to appear)].
Reviewer: V.Isakov (Wichita)

MSC:

35R30 Inverse problems for PDEs
35K55 Nonlinear parabolic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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