Consider a strictly hyperbolic n x n system of conservation laws in one space dimension: ut+f(u)x=0. Assuming that the initial data has small total variation, the global existence of weak solutions was proved by Glimm [9], while the uniqueness and stability of entropy admissible BV solutions was recently established in a series of papers [2 4 5 6 7 13]. See also [3] for a comprehensive presentation of these results. A long standing open question is whether these discontinuous solutions can be obtained as vanishing viscosity limits. More precisely, given a smooth initial data u¯:R↦Rn with small total variation, consider the parabolic Cauchy problem ut+A(u)ux=εuxx, u(0,x)=u¯(x).
Viscosity solutions for hyperbolic systems where shock curves are straight lines / Bianchini, S.; Bressan, A.. - 140:(2001), pp. 159-167. (Intervento presentato al convegno Hyperbolic problems: Theory, numerics, applications tenutosi a Magdeburg, Germany nel February/March 2000) [10.1007/978-3-0348-8370-2_17].
Viscosity solutions for hyperbolic systems where shock curves are straight lines
Bianchini, S.;
2001-01-01
Abstract
Consider a strictly hyperbolic n x n system of conservation laws in one space dimension: ut+f(u)x=0. Assuming that the initial data has small total variation, the global existence of weak solutions was proved by Glimm [9], while the uniqueness and stability of entropy admissible BV solutions was recently established in a series of papers [2 4 5 6 7 13]. See also [3] for a comprehensive presentation of these results. A long standing open question is whether these discontinuous solutions can be obtained as vanishing viscosity limits. More precisely, given a smooth initial data u¯:R↦Rn with small total variation, consider the parabolic Cauchy problem ut+A(u)ux=εuxx, u(0,x)=u¯(x).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
