Consider the nonlinear transport equation u t + c(u)u x = 0; x R ; t >
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Question:
Consider the nonlinear transport equation
ut + c(u)ux = 0; xR; t > 0
with initial condition u(0; x) = f(x).
1. Show that if c and f are both increasing or both decreasing, then there is no shock.
2. Using c(u) = u and
f(x)=1,x<01+x,0<x<12,x>1
find the solution. Draw the characteristics.
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
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