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Linear hyperbolic systems in domains with growing cracks

Show simple item record Caponi, Maicol 2017-01-30T11:27:21Z 2017-01-30T11:27:21Z 2017-01
dc.description.abstract We consider the hyperbolic system $\ddot u-{\rm div}\,(\mathbb A\nabla u)=f$ in the time varying cracked domain $\Omega\setminus\Gamma_t$, where the set $\Omega\subset\mathbb R^d$ is open, bounded, and with Lipschitz boundary, the cracks $\Gamma_t$, $t\in[0,T]$, are closed subsets of $\overline\Omega$, increasing with respect to inclusion, and $u(t):\Omega\setminus\Gamma_t\to\mathbb R^d$ for every $t\in[0,T]$. We assume the existence of suitable regular changes of variables, which reduce our problem to the transformed system $\ddot v-{\rm div}\,(\mathbb B\nabla v)+\mathbf a\nabla v -2\nabla\dot vb=g$ on the fixed domain $\Omega\setminus\Gamma_0$. Under these assumptions, we obtain existence and uniqueness of weak solutions for these two problems. Moreover, we show an energy equality for the functions $v$, which allows us to prove a continuous dependence result for both systems. en_US
dc.language.iso en en_US
dc.relation.ispartofseries SISSA;05/2017/MATE
dc.rights The author en_US
dc.subject second order linear hyperbolic systems en_US
dc.subject dynamic fracture mechanics en_US
dc.subject cracking domains en_US
dc.title Linear hyperbolic systems in domains with growing cracks en_US
dc.type Preprint en_US
dc.miur.area 1 en_US
dc.contributor.area Mathematics en_US

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