The paper deals with the investigation of a relaxation problem when time tends to infinity, for a hyperbolic conservation law wτ+f(w,z)y=0, zτ+g(w,z)y=h(w,z). It is assumed that the limits f∗(w)=limz→0f(w,z)/z and h∗(w)=limz→0h(w,z)/z, g0(w)=limz→0g(w,z) exist. Then it is proved that functions u and v which are rescaling transformations of w and z in space and in time converge to the solution of the reduced system ut+(f∗(u)v)x=0, g0(u)x=h∗(u)v that yields a parabolic problem for u.
Parabolic relaxation limit for hyperbolic systems of conservation laws 45, part I (1996), 393–406.
MARCATI, PIERANGELO;RUBINO, BRUNO
1996-01-01
Abstract
The paper deals with the investigation of a relaxation problem when time tends to infinity, for a hyperbolic conservation law wτ+f(w,z)y=0, zτ+g(w,z)y=h(w,z). It is assumed that the limits f∗(w)=limz→0f(w,z)/z and h∗(w)=limz→0h(w,z)/z, g0(w)=limz→0g(w,z) exist. Then it is proved that functions u and v which are rescaling transformations of w and z in space and in time converge to the solution of the reduced system ut+(f∗(u)v)x=0, g0(u)x=h∗(u)v that yields a parabolic problem for u.File in questo prodotto:
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