In this paper we are concerned with the study of the relaxation of the following system of balance laws: ut + f(u; v)x = 0; vt + g(u; v)x = 1 ((u) − v); (1) with u0(x), v0(x) ∈ L∞ and f, g and smooth functions (for instance, f, g and ∈ C5). We assume that the system is strictly hyperbolic, namely −(u; v) ¡ +(u; v); where −(u; v), +(u; v) are the two characteristic speeds of Eq. (1). We want to prove the convergence of the weak solutions of Eq. (1) toward the solutions of the scalar conservation law ut + f(u; (u))x = 0

The Zero Relaxation Limit for 2x2 Hyperbolic Systems

MARCATI, PIERANGELO
1999

Abstract

In this paper we are concerned with the study of the relaxation of the following system of balance laws: ut + f(u; v)x = 0; vt + g(u; v)x = 1 ((u) − v); (1) with u0(x), v0(x) ∈ L∞ and f, g and smooth functions (for instance, f, g and ∈ C5). We assume that the system is strictly hyperbolic, namely −(u; v) ¡ +(u; v); where −(u; v), +(u; v) are the two characteristic speeds of Eq. (1). We want to prove the convergence of the weak solutions of Eq. (1) toward the solutions of the scalar conservation law ut + f(u; (u))x = 0
Conservation laws, Hyperbolic systems, Relaxation problems
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12571/1924
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