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On solvability of an inverse problem with an unknown coefficient and right-hand side for a parabolic equation. (English) Zbl 1028.35168

Summary: We study the inverse problem for a parabolic equation \[ u_t-\Delta u+\lambda u+ q(x) u= a(x,t) q_0(x)+ f(x,t), \] in which the unknowns are the solution, coefficient of the function, and right-hand side (exterior load). We prove existence and uniqueness theorems.

MSC:

35R30 Inverse problems for PDEs
35K15 Initial value problems for second-order parabolic equations
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