Parabolic integrodifferential identification problems related to radial memory kernels II

Details Parabolic integrodifferential identification problems related to radial memory kernels II Parabolic integrodifferential identification problems related to radial memory kernels II

2006-07-13

arxiv.org/abs/math/0607312v1

J. Inverse Ill-Posed Probl. 9 (2001), no. 6, 595--614

Mathematics

Analysis of PDEs

18 pages

Scientific paper

We are concerned with the problem of recovering the radial kernel $k$, depending also on time, in the 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 ball or a disk.

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