This article is cited in 12 papers

The Cauchy problem for Shilov parabolic equations

V. A. Litovchenko

Chernivtsi National University named after Yuriy Fedkovych

Abstract: We establish well-posed solvability of the Cauchy problem for the Shilov parabolic equations with time-dependent coefficients whose initial data are tempered distributions. For a certain class of equations we state necessary and sufficient conditions for unique solvability of the Cauchy problem whose properties with respect to the spatial variable are typical for a fundamental solution. The results are characterized only by the order and the parabolicity exponent.

Keywords: Cauchy problem, Shilov parabolicity, $S$-type space, multiplier.

UDC: 517.55

Received: 10.10.2002

 English version: Siberian Mathematical Journal, 2004, 45:4, 669–679

Bibliographic databases:

• 
• 
•