Tsotne:
I worked through Walter Strauss' Partial Differential Equations. This serves as a good introduction. Are you particularly looking for a numerical PDE texts?
For a good stochastic PDE book, check out:
Harrison, J. Michael. Brownian Motion and Stochastic Flow Systems. Malabar, FL: Robert E. Krieger Pub. Co., 1990, chapter 4. ISBN: 0894644556.
Regards,
Joe