Complete Solvability of the Cauchy Problem for Petrovskii Parabolic Equations in S-Type Spaces

• Date: 2002
• Main Authors: Litovchenko, V. A., Літовченко, В. А.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2002
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4185
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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.