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Uniqueness for an inverse source problem of determining a space dependent source in a non-autonomous parabolic equation

2020; Elsevier BV; Volume: 107; Linguagem: Inglês

10.1016/j.aml.2020.106395

1873-5452

Marián Slodička,

Stability and Controllability of Differential Equations

We study uniqueness for an inverse source problem for a second order parabolic equation ∂tu(x, t) + A(t)u(x, t) = h(t)f (x) with time dependent coefficients.The unknown space dependent source f (x) is determined from the final time overdetermination.New uniqueness results are formulated in Theorems 2.1 and 3.1, assuming 0 ̸ ≡ h ≥ 0.