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- W86125560 abstract "The model one-dimensional conservation law with discontinuous spatially heterogeneous flux is EvPb $$displaystyle{ u_{t} + mathfrak{f}(x,u)_{x} = 0,quad mathfrak{f}(x,cdot ) = {f}^{l}(x,cdot )1!!1_{ x<0}! + {f}^{r}(x,cdot )1!!1_{ x>0}. }$$ We prove well-posedness for the Cauchy problem for (EvPb) in the framework of solutions satisfying the so-called adapted entropy inequalities.Exploiting the notion of integral solution that comes from nonlinear semigroup theory, we propose a way to circumvent the use of strong interface traces for the evolution problem (EvPb) (in fact, proving the existence of such traces for the case of x-dependent f l,r would be a delicate technical issue). The difficulty is shifted to the study of the associated one-dimensional stationary problem $$u + mathfrak{f}(x,u)_{x} = g$$ , where the existence of strong interface traces of entropy solutions is an easy fact. We give a direct proof of this, avoiding the subtle arguments of the kinetic formulation (Kwon YS, Vasseur A (2007) Arch Ration Mech Anal 185(3):495–513) and of the H-measure approach (Panov EY (2007) J Hyperbolic Differ Equ 4(4):729–770)." @default.
- W86125560 created "2016-06-24" @default.
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- W86125560 date "2013-08-28" @default.
- W86125560 modified "2023-10-16" @default.
- W86125560 title "The Semigroup Approach to Conservation Laws with Discontinuous Flux" @default.
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- W86125560 doi "https://doi.org/10.1007/978-3-642-39007-4_1" @default.
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