Complete Solvability of the Cauchy Problem for Petrovskii Parabolic Equations in <em class="a-plus-plus">S</em>-Type Spaces

Abstract

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.