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 ?**


Thanks.



Reference request: Spectral analysis of advection diffusion PDE
I am not sure whether there has been a comprehensive study of spectral properties of such equations, but you may be interested in the paper ``Diffusion and Mixing in Fluid Flow'' by Constantin, Kiselev, Ryzhik and Zlatos and the references therein. 


<http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.76.6407>


An online version can be found here:


<http://math.stanford.edu/~ryzhik/ckrz.pdf>


