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.
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Litovchenko, V.A. Complete Solvability of the Cauchy Problem for Petrovskii Parabolic Equations in S-Type Spaces. Ukrainian Mathematical Journal 54, 1778–1793 (2002). https://doi.org/10.1023/A:1024088207271
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DOI: https://doi.org/10.1023/A:1024088207271