Inverse problems of the determination of the coefficient in parabolic equations. I
The authors prove uniqueness theorems for the determination of \(c(x)\) in the equation \[ u_ t-Lu=cu+g \] resp. the determination of \(\rho(x)\) in the equation \[ \rho u_ t-Lu=g \] on \(\Omega \times (0,T)\), \(\Omega\) a bounded domain in \(\mathbb{R}^ n\), \(L\) an elliptic operator of the second order. Besides, an initial condition, a boundary condition on \(\partial \Omega \times [0,T]\) of Dirichlet type or type \(\partial u/ \partial \nu+\sigma(x)u\), and additionally \(u(x,t_ 1)\) for \(x \in \Omega\) and a fixed \(t_ 1\), \(0<t_ 1 \leq T\), or \(\int^ T_ 0u(x,\tau) \omega(\tau)d \tau\) are given.
scientific article; zbMATH DE number 130813
scientific article