Let v E C1(R) and consider the equation dt(u) + dx(uv) = 0, x E R, t>0, u(x,0) = u0(x), x E R, We assume that v satisfies v(x) > 0, v’ (x) > 0 for all x E R. Prove that sup|u(x,t)| < sup|u0(x)| for all t > 0
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