Name
Abstract | ||
|---|---|---|
We characterize the vanishing viscosity limit for multi-dimensional conservation laws of the form u(t) + div f(x, u) = 0, u|(t=0) = u(0) in the domain R+ x R-N. The flux f = f(x, u) is assumed locally Lipschitz continuous in the unknown u and piecewise constant in the space variable x; the discontinuities of f(., u) are contained in the union of a locally finite number of sufficiently smooth hypersurfaces of R-N. We define "G(VV)-entropy solutions" (this formulation is a particular case of the one of [3]); the definition readily implies the uniqueness and the L-1 contraction principle for the G(VV)-entropy solutions. Our formulation is compatible with the standard vanishing viscosity approximation u(t)(epsilon) + div (f(x, u(epsilon))) = epsilon Delta u(epsilon), u(epsilon)|(t=0) = u(0), epsilon down arrow 0, of the conservation law. We show that, provided u(epsilon) enjoys an epsilon-uniform L-infinity bound and the flux f(x, .) is non-degenerately nonlinear, vanishing viscosity approximations u(epsilon) converge as epsilon down arrow 0 to the unique G(VV)-entropy solution of the conservation law with discontinuous flux. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.3934/nhm.2010.5.617 | NETWORKS AND HETEROGENEOUS MEDIA |
Keywords | Field | DocType |
multidimensional hyperbolic scalar conservation law,entropy solution,discontinuous flux,boundary trace,vanishing viscosity approximation,admissibility of solutions | Uniqueness,Mathematical optimization,Finite set,Mathematical analysis,Contraction principle,Viscosity,Lipschitz continuity,Flux,Mathematics,Conservation law | Journal |
Volume | Issue | ISSN |
5 | 3 | 1556-1801 |
Citations | PageRank | References |
3 | 0.43 | 5 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Boris Andreianov | 1 | 27 | 5.70 |
| Kenneth H. Karlsen | 2 | 119 | 23.76 |
| Nils Henrik Risebro | 3 | 79 | 38.95 |