As the title says, I am looking for a authoritative reference/monograph on this topic. My interest is in spectral properties of this PDE, and NOT on existence/uniqueness etc. which is usually the focus of most theoretical PDE texts. NOT on numerical methods to solve the PDE, which is usually the focus of engineering/physics PDE texts.
My motivation is to understand the various functional analytic aspects of this PDE under varying conditions: e.g. change in the spectrum when changing the advective component from something "regular" to chaotic, dependence of spectrum on bounded Vs unbounded flows, dependence on diffusivity etc.
I have been trying to read recent literature on such equations, and I haven't found a single solid source which has all the basic results on spectral properties of such equations.
Is there a recent book or monograph which focuses on spectral theory of (linear or nonlinear) parabolic PDEs in general, or advection-diffusion equations in particular ?