Daniela Sforza

Daniela Sforza
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Daniela Sforza

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Mathematics - Analysis of PDEs (2)

Publications Authored By Daniela Sforza

We consider an anisotropic hyperbolic equation with memory term: $$ \partial_t^2 u(x,t) = \sum_{i,j=1}^n \partial_i(a_{ij}(x)\partial_ju) + \int^t_0 \sum_{| \alpha| \le 2} b_{\alpha}(x,t,\eta)\partial_x^{\alpha}u(x,\eta) d\eta + F(x,t) $$ for $x \in \Omega$ and $t\in (0,T)$ or $\in (-T,T)$, which is a model equation for viscoelasticity. First we establish a Carleman estimate for this equation with overdetermining boundary data on a suitable lateral subboundary $\Gamma \times (-T,T)$. Second we apply the Carleman estimate to establish a both-sided estimate of $| u(\cdot,0)|_{H^3(\Omega)}$ by $\partial_{\nu}u|_{\Gamma\times (0,T)}$ under the assumption that $\partial_tu(\cdot,0) = 0$ and $T>0$ is sufficiently large, $\Gamma \subset \partial\Omega$ satisfies some geometric condition. Read More

We investigate control problems for wave-Petrovsky coupled systems in the presence of memory terms. By writing the solutions as Fourier series, we are able to prove Ingham type estimates, and hence reachability results. Our findings have applications in viscoelasticity theory and linear acoustic theory. Read More