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Mat. Zametki, 2007, Volume 82, Issue 6, Pages 850–872 (Mi mz4185)  

Cauchy Problem for Parabolic Systems with Convolution Operators in Periodic Spaces

V. A. Litovchenko

Chernivtsi National University named after Yuriy Fedkovych

Abstract: For a class of periodic systems of parabolic type with pseudodifferential operators containing $\{\vec p,\vec h\}$-parabolic systems of partial differential equations, we study the properties of the fundamental matrices of the solutions and establish the well-posed solvability of the Cauchy problem for these systems in the spaces of generalized periodic functions of the type of Gevrey ultradistributions. For a particular subclass of systems, we describe the maximal classes of well-posed solvability of the Cauchy problem.

Keywords: Cauchy problem, parabolic system, Gevrey ultradistribution, convolution operator, periodic space, Weyl operator, trigonometric Fourier series, Banach space

DOI: https://doi.org/10.4213/mzm4185

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English version:
Mathematical Notes, 2007, 82:6, 766–786

Bibliographic databases:

UDC: 517.928
Received: 23.06.2006

Citation: V. A. Litovchenko, “Cauchy Problem for Parabolic Systems with Convolution Operators in Periodic Spaces”, Mat. Zametki, 82:6 (2007), 850–872; Math. Notes, 82:6 (2007), 766–786

Citation in format AMSBIB
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