Parabolic integrodifferential identification problems related to radial memory kernels I

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

2006-07-13

arxiv.org/abs/math/0607311v1

J. Inverse Ill-Posed Probl. 9 (2001), no. 5, 489--529

Mathematics

Analysis of PDEs

36 pages

Scientific paper

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.

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