Abstract:
The problem of defining δ-shock wave type solutions of
hyperbolic systems of conservation laws in connection with the constructing
singular superpositions products of distributions is studied. We illustrate this problem
by constructing δ-shock wave type solutions for two systems. One of them,
ut+ (f(u)-v)x=0,
vt+ g(u)x=0,
is a generalization of the well-known Keyfitz--Kranzer system,
where f(u) and g(u) are polynomials of degree n and
n+1, respectively, n is an even integer.
The other one is the system
ut+f(u)x=0,
vt+(vg(u))x=0,
where f(u), g(u) are smooth functions.
As far as we know, exact -shock wave type solutions
for the first system have never been constructed.