The problem I have to solve is the following:
$\frac{\partial p}{\partial t} -c \frac{\partial ^2p}{\partial x^2}=0 \quad \quad (x,t) \in (0,L)\times[0,\infty)$
with
$\frac{\partial p}{\partial x}(x=0,t) =Q \quad \quad t>0$
$\frac{\partial p}{\partial x}(x=L,t) =0 \quad \quad t>0$
$p(x, t=0)=0 \quad \quad x \in (0,L)$
where Q is a constant.
So, there are two different Neumann boundary conditions, and a zero initial condition.
I tried to solve by separation of variables but I'm stuck at this stage, as I don't know how to impose the boundary conditions and the initial condition. I suspect I should use Fourier series but I don't really understand how to do it when the initial condition is 0.
Could someone help me with that? Thank you!