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- Solve Burgers' equation 1 answer
Solve the following partial differential equation $u_t + uu_x=0$ with $u=u(x,t)$ and $u(x,0)=x$.
I am having trouble in applying the SIDE CONDITION.
- The Characteristics are $dx/dt$=$u$, here u is constant along the characteristics.
- Along the characteristics $dx/dt=g(x_o)$
- Solution is $x=g(X_o)t + d$, where d is an arbitary constant
- But note at $t=0$, $x=x_0$...Hence $d=x_0$
- The Characteristics is $x=g(x_0)t + x_0$, these are straight lines with variable slope
I am not sure on what to do after this point.