Question

Need help on math modeling problems regarding linear partial differential equation

67.3. Suppose initially (t = 0) that the traffic density is p = Do + Esin , where le « po. Determine p(x, t). 67.4. Consider Õpildt + copildx) = 0. Suppose we observe pi in a coordinate system moving at velocity v. Show that др. +(c dr 0. v) dx' Does p stay constant moving at the car velocity? 67.5. Based on a linear analysis, would you say p = po, a constant, is a stable or unstable equilibrium solution of equation 66.1? api

Answer 1

279 요 - Po 941 La (Pote frica, where IEILPo. 184-4-2 ZLO la 270 x-940 -of-s-ca-a) -(2-a) La [ x-a 2a70 2-a So bere le LLP so we take to axa say 27 1, 2, 3, P-Po and 22112,3 --- Po Pote where ELLA. say Po=2, these can be 0.01 P(2) @s at tao. Z -T 2 34 -3 b) at t=2 PC2) PO 42 peo

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