Existence and uniqueness for a nonlinear parabolic/Hamilton-Jacobi coupled system describing the dynamics of dislocation densities
| dc.creator | Ibrahim, Hassan | |
| dc.date | 2007-03-27 | |
| dc.date.accessioned | 2026-07-07T07:54:06Z | |
| dc.date.available | 2026-07-07T07:54:06Z | |
| dc.description | We study a mathematical model describing the dynamics of dislocation densities in crystals. This model is expressed as a one-dimensional system of a parabolic equation and a first order Hamilton-Jacobi equation that are coupled together. We show the existence and uniqueness of a viscosity solution among those assuming a lower-bound on their gradient for all time including the initial data. Moreover, we show the existence of a viscosity solution when we have no such restriction on the initial data. We also state a result of existence and uniqueness of an entropy solution of the system obtained by spatial derivation. The uniqueness of this entropy solution holds in the class of ``bounded from below'' solutions. In order to prove these results, we use a relation between scalar conservation laws and Hamilton-Jacobi equations, mainly to get some gradient estimates. This study takes place on $\R$, and on a bounded domain with suitable boundary conditions. | |
| dc.identifier | https://arxiv.org/abs/math/0703783 | |
| dc.identifier | http://arxiv.org/abs/math/0703783 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/126472 | |
| dc.subject | Analysis of PDEs | |
| dc.title | Existence and uniqueness for a nonlinear parabolic/Hamilton-Jacobi coupled system describing the dynamics of dislocation densities | |
| dc.type | text |