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The following is the well-known nonlinear differential equation for director's distribution at static equilibrium in liquid crystal displays(LCD). I want to obtain weak form of the given differential ...

How to solve the third order time dependent partial differential equation $$u_t + 6u_x + u_xxx = 0$$ in weak form using galerkin finite element method?

I am trying to solve a 4th order boundary value problem with variable coefficients, namely the problem of a rotating cantilever beam: $u'''' - \frac{((1-x^2)u')'}{2\eta} - \frac{\alpha}{\eta}((1-x)u')...

Suppose we are dealing with diffusion over a boundaryless manifold $M$ (for simplicity let's say it's a surface). In that case, we have \begin{align} \int_M W \Delta U \mathrm{d} x & = -\int_M \...