We are concerned with the problem of recovering the radial kernel $k$, depending also on time, in a parabolic integro-differential equation $$D_{ t}u(t,x)={ \cal A}u(t,x)+\int_0^t k(t-s,|x|){ \cal B}u(s,x)ds +\int_0^t D_{ |x|}k(t-s,|x|){ \cal C}u(s,x)ds+f(t,x),$$ ${ \cal A}$ being a uniformly elliptic second-order linear operator in divergence form. We single out a special class of operators ${ \cal A}$ and two pieces of suitable additional information for which the problem of identifying $k$ can be uniquely solved locally in time when the domain under consideration is a spherical corona or an annulus.
Categories: math.AP