I have been confronted with a partial differential equation of the following form \begin{equation} \frac{\partial u}{\partial t} -c\frac{\partial u}{\partial x} + ax^2 \frac{\partial u^2}{\partial x^2} = 0 \end{equation} with two of the boundary conditions being $u(x,0)=0$ and $u(0,t)=0$. Of course I also need a third boundary condition to get a unique solution. Is it possible to solve this and get a somewhat analytical solution. I tried Laplace transform but that didn't seem to help much.
The partial differential equation $\frac{\partial u}{\partial t} -c\frac{\partial u}{\partial x} + ax^2 \frac{\partial u^2}{\partial x^2} =0$
1
$\begingroup$
pde
-
1did you try seperation of variables? – 2017-01-26
-
0No, since I have a dirichlet condition for as an initial condition. – 2017-01-26
-
0what difference does this make? – 2017-01-26
-
0I will only get the trivial solution. – 2017-01-26
-
0why is that? this is interesting – 2017-01-26
-
0Because the solution is either not separable, or my modelling is wrong and the trivial solution is the only solution? – 2017-01-26
-
0Let us [continue this discussion in chat](http://chat.stackexchange.com/rooms/52550/discussion-between-freelunch-and-tired). – 2017-01-26