quasi- linear equation(curve of discontinuous solution )

Question

Help me please to solve this equation: $u_{t}+c\left [ u(1-u) \right ]_{x}=0$ in [a,b]

$c$ is constant. Find smooth boundary and initial conditions when the solution is discontinuous .

Thanks a lot!

On which domain do you consider your equation? Is there any correspondance between $q$ and $u$? Is $c$ constant?
@martini Oh, thanks. It's no q just u, in[a,b], and indeed c is constant

doraemonpaul · Accepted Answer · 2012-07-19 14:44:46Z

up vote 1 down vote accepted

$u_t+c[u(1-u)]_x=0$

$u_t+c[u-u^2]_x=0$

$u_t+c(u_x-2uu_x)=0$

$u_t+c(1-2u)u_x=0$

So the general solution is $x=ct(1-2u)+C(u)$

answered Jul 19 '12 at 14:44

doraemonpaul
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