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Solvability of an inverse problem for the parabolic equation with convergence. (English. Russian original) Zbl 0784.35123
Sib. Math. J. 33, No. 3, 402-408 (1992); translation from Sib. Mat. Zh. 33, No. 3, 42-49 (1992).
The evolution equation $$u_ t=L(x)u+q(x)u+f(x,t)$$, $$L$$ a second order elliptic operator, is considered on $$\Omega \times(-\infty,+\infty)$$, $$\Omega \subset \mathbb{R}^ n$$, with a Dirichlet boundary condition on $$\partial \Omega \times(-\infty,+\infty)$$. If $$u(x,0)=u_ 0(x)$$ is given the author provides criteria concerning the unique solvability of the coefficient determination problem for $$q(x)$$.
##### MSC:
 35R30 Inverse problems for PDEs 35K20 Initial-boundary value problems for second-order parabolic equations