arXiv subjects

A. Favaron

Publications and source records attributed to A. Favaron.

3 recordsLinked to original sources

arXiv2006

Generation type inequalities for closed linear operators related to domains with conical points

Let ${\cal A}(x;D_x)$ be a second-order linear differential operator in divergence form. We prove that the operator $łI- {\cal A}(x;D_x)$, where $ł\in\csp$ and $I$ stands for the identity operator, is closed and injective when ${\rm Re}ł$ is large enough and the domain of ${\cal A}(x;D_x)$ consists of a special class of weighted Sobolev function spaces related to conical open bounded sets of $\rsp^n$, $n \ge 1$.

math.AP↗

arXiv2006

Parabolic integrodifferential identification problems related to radial memory kernels I

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.

math.AP↗

arXiv2006

Parabolic integrodifferential identification problems related to radial memory kernels II

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.

math.AP↗