I am looking for a reference where well-posedness of problems $$u_t + A(t)u = f$$ is addressed via the Galerkin method where $A$ is a pseudomonotone operator. I am aware that Roubicek's book Nonlinear partial differential equations with applications has this but the presentation leaves a lot to be desired.
Let me emphasise that I'd ideally like a solution using the Galerkin method. Does anyone know any good sources? Thank you!
PS: if this is not possible, other suggestions are welcome too. But I am keen to use a Sobolev space setting.
