Ukrainian Mathematical Bulletin

Volume 4, Issue 3, 2007 pp. 389-414.

The Cauchy Problem for a Certain Class of Pseudodifferential Systems in Spaces of Periodic Functions

Authors: Vladyslav A. Litovchenko
Author institution: Yuri Fed'hovych Chernivtsi National University, vul. Kotsyubyns'kogo 2, 58012, Chernivtsi, Uktraine vladlit@chnu.cv.ua

Summary: For a certain class of pseudodifferential systems, we study properties of fundamental matrices of solutions, prove correct solvability of the Cauchy problem for these systems in the spaces of generalized periodic functions of the Gevrey ultradistribution type. For a certain subclass of systems that contains periodic $2\overrightarrow{b}$-parabolic systems with coefficients depending only on time, we describe maximal classes of correct solvability of the Cauchy problem.

Contents Full-Text PDF