Carleman estimates for integro-differential parabolic equations with singular memory kernels

01 Pubblicazione su rivista
Loreti Paola, Sforza Daniela, Yamamoto Masahiro
ISSN: 2296-9020

On the basis of the Carleman estimate for the parabolic equation, we prove a Carleman estimate for the integro-differential operator
$\partial_t-\triangle+\int_0^t K(x,t,r)\triangle\ dr$
where the integral kernel has a behaviour like a weakly singular one.
In the proof we consider the integral term as a perturbation. The crucial point is
a special choice of the time factor of the weight function.

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