We consider the Cauchy problem for a n×n strictly hyperbolic system
of balance laws {arraycut+f(u)x=g(x,u),x∈R,t>0u(0,.)=uo∈L1∩BV(R;Rn),∣λi(u)∣≥c>0foralli∈{1,...,n},∥g(x,⋅)∥C2≤M~(x)∈L1,array. each characteristic field being genuinely nonlinear or linearly
degenerate. Assuming that the L1 norm of
∥g(x,⋅)∥C1 and \|u_o\|_{BV(\reali)} are small enough, we
prove the existence and uniqueness of global entropy solutions of bounded total
variation extending the result in [1] to unbounded (in L∞) sources.
Furthermore, we apply this result to the fluid flow in a pipe with
discontinuous cross sectional area, showing existence and uniqueness of the
underlying semigroup.Comment: 26 pages, 4 figure
We prove a rigorous convergence result for the compressible to incompressible
limit of weak entropy solutions to the isothermal 1D Euler equations.Comment: 16 page