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On the inverse problem of determining the right-hand side of a parabolic equation under an integral overdetermination condition. (English. Russian original) Zbl 1075.35106
Math. Notes 77, No. 4, 482-493 (2005); translation from Mat. Zametki 77, No. 4, 522-534 (2005).
Summary: We study the unique solvability of the inverse problem of determining the right-hand side of a parabolic equation \[ \rho(t,x)u_t-\Delta u=f(x)g(t,x)+h(t,x) \] whose leading coefficient depends on both the time and the spatial variable under an integral overdetermination condition with respect to time. We obtain two types of condition sufficient for the local solvability of the inverse problem as well as study the so-called Fredholm solvability of the inverse problem under consideration.

35R30 Inverse problems for PDEs
35K15 Initial value problems for second-order parabolic equations
Full Text: DOI
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