Texts for eigenvalues, eigenvectors & pde's

diaw (Des Aubery)

I am presently researching the role of eigenvalues, eigenvectors & their role in PDE's. I have read through a number of general Math texts, but am looking for something more in-depth with application to fluid PDE's.

I have performed some extremely interesting simulations & would like to check the background theory more thoroughly.

I would really value a few good pointers to advanced texts & papers.

Many thanks, diaw...