Concentration of source terms in generalized Glimm scheme for global entropy solutions of nonlinear hyperbolic balance laws

Global existence and strong trace property of entropy solutions by the source-concentration Glimm scheme for nonlinear hyperbolic balance laws

“…In general, there exist some technical difficulties to employ the concerntration method to construct the approximate solutions due to the low regularity of the solutions in nonlinear balance laws. The results of this paper, together with the ones of [2,8] indicates that the source-concentration method also holds in the hyperbolic system of balance laws.…”

“…Following a similar argument as section 4 in [2], one can easily find that U θ (x, t) is an entropy solution to (1.3) for almost every sampling sequence θ. We leave the detail to the readers.…”

“…The technique of asymptotic expansion to a in [18] also fails in our case. To overcome this difficulty, Chou-Lin [2] choose 0 < ε 1, decompose D κδ into the following six sub-regions:…”

“…And I 2 is called an immediate successor of I 1 if I 2 > I 1 and they differ by a single polygonal region. The wave interaction estimates on the single interior hexagonal region Γ centered at (x m , t p ) were given in [2]. To state it, we let…”

“…where C 0 is the constant in Theorem 3.1. It is easy to see that L(I) is equivalent to the total variation of U ε θ,Δx on I and Q(I) ≤ L(I) 2 .…”