I'll pay FG for a PDF of any of these:
Petrowsky, I. G. (1996), Oleinik, O. A., ed., Selected works. Part II: Differential equations and probability theory, Classics of Soviet Mathematics, 5 (part 2), Amsterdam: Gordon and Breach Publishers, ISBN 2-88124-979-5
[There's a preview in Google, but it cuts out some pages I need]
Petrovsky, I. G. (1935), Zur ersten Randwertaufgabe der Wärmeleitungsgleichung [English translation, which I know exists, but isn't available to my library]
The author is Russian, English translations have spelled it lots of different ways: Petrowsky, Petrovky, Petrovskii, etc.