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!
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!
$u_t+c[u(1-u)]_x=0$
$u_t+c[u-u^2]_x=0$
$u_t+c(u_x-2uu_x)=0$
$u_t+c(1-2u)u_x=0$
This belongs to a PDE of the form http://eqworld.ipmnet.ru/en/solutions/fpde/fpde2203.pdf
So the general solution is $x=ct(1-2u)+C(u)$