This article is cited in 7 papers

The Cauchy problem for one class of parabolic pseudodifferential systems with nonsmooth symbols

V. A. Litovchenko

Chernivtsi National University named after Yuriy Fedkovych

Abstract: In the class of finite-order distributions we establish the well-posedness of the Cauchy problem for parabolic pseudodifferential systems whose symbols are nonsmooth functions at a fixed point $h\in\mathbb R^n$ generated by homogeneous functions of order $\gamma>0$ depending on time.

Keywords: Cauchy problem, pseudodifferential system, nonsmooth symbol, convolution, distribution, matriciant.

UDC: 517.956.4

Received: 15.02.2006
Revised: 05.10.2007

 English version: Siberian Mathematical Journal, 2008, 49:2, 300–316

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