3.1 Consider the conservation equation with a constant velocity c > 0, +c = 0,...

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3.1 Consider the conservation equation with a constant velocity c > 0, ди +c = 0, Əx ди at on the quadrant t≥ 0, x ≥ 0. Suppose the boundary and initial conditions are for g, h = C¹[0, 00). [u(0, x) = g(x), x ≥ 0. u(t,0)=h(t), t≥0, (a) Find a formula for the solution u(t, x) in terms of g and h. (b) Find a matching condition for g and h that will ensure that u(t, x) is a C¹ function. 3.1 Consider the conservation equation with a constant velocity c > 0, ди +c = 0, Əx ди at on the quadrant t≥ 0, x ≥ 0. Suppose the boundary and initial conditions are for g, h = C¹[0, 00). [u(0, x) = g(x), x ≥ 0. u(t,0)=h(t), t≥0, (a) Find a formula for the solution u(t, x) in terms of g and h. (b) Find a matching condition for g and h that will ensure that u(t, x) is a C¹ function.

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