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The determination of a parabolic equation from initial and final data. (English) Zbl 0644.35093
The author studies an inverse problem relative to the parabolic equation $$ u\sb t-\Delta u+a(x)u=0,\quad (x,t)\in \Omega \times (0,T), $$ $$ \partial u/\partial n=0,\quad (x,t)\in \partial \Omega \times (0,T),\quad u(x,0)=f(x). $$ The additional information is $u(x,T)=g(x)$. Under certain conditions there is at most one solution pair (a,u) to the problem considered. It is a “folk-theorem” in undetermined coefficient problems that one gets a well-posed problem if the additional data is prescribed in a direction “parallel” to the coefficient but not if it is “perpendicular”. See also {\it S. Handrock-Meyer}, Inverse problems for the heat equation (German), to appear in Zeitschrift für Analysis und ihre Anwendungen.
Reviewer: G.Anger

35R30Inverse problems for PDE
35K15Second order parabolic equations, initial value problems
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