Viscosity solutions of Hamilton--Jacobi equations with discontinuous coefficients
| dc.creator | Coclite, Giuseppe Maria | |
| dc.creator | Risebro, Nils Henrik | |
| dc.date | 2003-03-24 | |
| dc.date.accessioned | 2026-07-07T04:56:18Z | |
| dc.date.available | 2026-07-07T04:56:18Z | |
| dc.description | We consider Hamilton--Jacobi equations, where the Hamiltonian depends discontinuously on both the spatial and temporal location. Our main results are the existence and well--posedness of a viscosity solution to the Cauchy problem. We define a viscosity solution by treating the discontinuities in the coefficients analogously to ``internal boundaries''. By defining an appropriate penalization function, we prove that viscosity solutions are unique. The existence of viscosity solutions is established by showing that a sequence of front tracking approximations is compact in $L^\infty$, and that the limits are viscosity solutions. | |
| dc.description | 20 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0303288 | |
| dc.identifier | http://arxiv.org/abs/math/0303288 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66873 | |
| dc.subject | Analysis of PDEs | |
| dc.title | Viscosity solutions of Hamilton--Jacobi equations with discontinuous coefficients | |
| dc.type | text |