Ukrainian Mathematical Bulletin

Volume 3, Issue 1, 2006 pp. 63-94.

The Cauchy Problem for One Class of Pseudo-differential Equations with Smooth Symbols

Authors: Vladislav A. Litovchenko
Author institution: Chernivets'kyi Yuri Fed'kovych National University vul. Kotsyubyns'kogo, 2, 58012, Chernivtsi, Ukraine, vladlit@chnu.cv.ua

Summary: For one class of pseudo-differential operators with smooth time dependent symbols, we study properties of fundamental solutions, formulate sufficient and, in some cases, also necessary conditions for the Cauchy problem with generalized initial conditions to be correctly solved. We also establish a localization principle for solutions of such problems. We construct spaces of test functions, which generalize certain classical spaces.

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