For a Hamilton-Jacobi equation defined on a network, we introduce its vanishing viscosity approximation. The elliptic equation is given on the edges and coupled with Kirchhoff-type conditions at the transition vertices. We prove that there exists exactly one solution of this elliptic approximation and mainly that, as the viscosity vanishes, it converges to the unique solution of the original problem. © 2013 Elsevier Inc.
The vanishing viscosity limit for Hamilton-Jacobi equations on networks / Camilli, Fabio; Claudio, Marchi; Dirk, Schieborn. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 254:10(2013), pp. 4122-4143. [10.1016/j.jde.2013.02.013]
The vanishing viscosity limit for Hamilton-Jacobi equations on networks
CAMILLI, FABIO;
2013
Abstract
For a Hamilton-Jacobi equation defined on a network, we introduce its vanishing viscosity approximation. The elliptic equation is given on the edges and coupled with Kirchhoff-type conditions at the transition vertices. We prove that there exists exactly one solution of this elliptic approximation and mainly that, as the viscosity vanishes, it converges to the unique solution of the original problem. © 2013 Elsevier Inc.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
