Assignment Questions-
Q1. Consider the equation
ut + (u4/4)x = 0
Find the admission solution for each of the following initial data:
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Q2. Consider the hyperbolic system
ut + uv= = u√v,
vt + vux = v√u,
and u, v > 0. Determine the characteristics and the corresponding ODEs. Show that along one of the characteristics, the following Riemann invariant holds
√u - √v = const.