Complete Solvability of the Cauchy Problem for Petrovskii Parabolic Equations in S-Type Spaces - Litovchenko, V. A. (Ukrains’kyi Matematychnyi Zhurnal, 2002)
We establish the correct solvability (in both directions) of the Cauchy problem for Petrovskii parabolic equations with time-dependent coefficients in S-type spaces. We also prove that a solution of this problem stabilizes to zero in the sense of the topology of these spaces.