I have derived the following PDE: $$\frac{\partial^2{u}}{\partial{t}^2} - \frac{\partial^2{u}}{\partial{y}^2} + \frac{\partial{u}}{\partial{t}} = 0$$ Boundary and initial conditions $$u(0,t) = 0, \hspace{5mm} u(H,t) = A\cdot cos(\omega\cdot t) \\\\ u(x,0) = 0$$
My inital approach would have been to use the method of seperation $$u(x,t) = X(x)\cdot T(t)$$ but I don't know how to deal with time dependent Boundary conditions. Can somebody help me out.
