Linear hyperbolic systems in domains with growing cracks
| dc.contributor.area | Mathematics | en_US |
| 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.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.identifier.uri | https://openscience.sissa.it/handle/1963/35271 | |
| dc.language.iso | en | en_US |
| dc.miur.area | 1 | 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 |