Identification of Memory Kernels Depending on Time and on an Angular Variable

We deal with the problem of recovering a memory kernel k(t, ), depending on time t and on an angular variable , in a parabolic integrodifferential equation related to a toric domain. We show that the problem can be uniquely solved locally in time if the kernel k is not assumed to be necessarily periodic with respect to . On the contrary, under a periodicity condition for k(t, ), we show uniqueness assuming existence.

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