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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.
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,
The tangential condition was introduced in [Hanke et al., 95] as a sufficient condition for convergence of the Landweber iteration for solving ill-posed problems. In this paper we present a series of time dependent benchmark inverse problems for which we can verify this condition.
We study the obstacle problem for parabolic operators of the type $partial_t + L$, where $L$ is an elliptic integro-differential operator of order $2s$, such as $(-Delta)^s$, in the supercritical regime $s in (0,frac{1}{2})$. The best result in this
In this paper we consider the homogenization of the evolution problem associated with a jump process that involves three different smooth kernels that govern the jumps to/from different parts of the domain. We assume that the spacial domain is divide
In this paper we consider second order parabolic partial differential equations subject to the Dirichlet boundary condition on smooth domains. We establish weighted $L_{q}$-maximal regularity in weighted Triebel-Lizorkin spaces for such parabolic pro