Find solutions to the Riemann Problems

i) Find the solution to the Riemann Problem for
$u_t + (u^3)_x = 0$
$U_L = 2$ and $U_R = 1$

ii) Find the solution to the Riemann Problem for
$v_t + 3/2 (v^4)_x = 0$
$V_L = 4$ and $V_R = 1$

iii) Show that $v = u^2$ with u from (i) formally solves (ii). Hint: multiply (i) by $u$.

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