Complete Solvability of the Cauchy Problem for Petrovskii Parabolic Equations in S-Type Spaces
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.
English version (Springer): Ukrainian Mathematical Journal 54 (2002), no. 11, pp 1778-1793.
Citation Example: Litovchenko V. A. Complete Solvability of the Cauchy Problem for Petrovskii Parabolic Equations in S-Type Spaces // Ukr. Mat. Zh. - 2002. - 54, № 11. - pp. 1467-1479.