SISSA Open Science

# Linear hyperbolic systems in domains with growing cracks

 dc.contributor.author Caponi, Maicol dc.date.accessioned 2017-01-30T11:27:21Z dc.date.available 2017-01-30T11:27:21Z dc.date.issued 2017-01 dc.identifier.uri http://preprints.sissa.it/xmlui/handle/1963/35271 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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