Consider the homogeneous convection equation ди au + c = 0 x>0, at ar t> 0 with the initial and boundary conditions u(0,

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Consider the homogeneous convection equation ди au + c = 0 x>0, at ar t> 0 with the initial and boundary conditions u(0,t) = 0 u(x,0) = f(x) = e-200(2–0.25)2 =e A.1 Use the technique in d'Alembert's solution by introducing the new independent variables v=x + ct w=c- ct and show that u(x, t) = f(x – ct).