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Ct+CCx = 0. que for any choice of

Ct+CCx = 0. que for any choice of

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Consider pt+F, = 0 for some smooth flux function F(p) and define the characteristic wave speed as c(p) = F'(p) such that pt + c(p)Pz = 0.. Show that for strong solutions the inviscid Burgers equation holds for c(x, t), i.e., Ct + cCx = 0. For strong solutions this is true for any choice of a smooth F(p). In the traffic model case F(p) = p – p². Now show that the weak solutions of (2) based on the conservation of f cdx are also identical to those of (1) based on the conservation of J p dx. (Hint: compare the shock speeds.)
Transcribed Image Text:Consider pt+F, = 0 for some smooth flux function F(p) and define the characteristic wave speed as c(p) = F'(p) such that pt + c(p)Pz = 0.. Show that for strong solutions the inviscid Burgers equation holds for c(x, t), i.e., Ct + cCx = 0. For strong solutions this is true for any choice of a smooth F(p). In the traffic model case F(p) = p – p². Now show that the weak solutions of (2) based on the conservation of f cdx are also identical to those of (1) based on the conservation of J p dx. (Hint: compare the shock speeds.)
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