Geodesic
Cauchy Problem for Parabolic Systems with Convolution Operators in Periodic Spaces
Matematičeskie zametki, Tome 82 (2007) no. 6, pp. 850-872.

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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, convolution operator, periodic space, Weyl operator, trigonometric Fourier series, Banach space.
Mots-clés : Gevrey ultradistribution 
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V. A. Litovchenko. Cauchy Problem for Parabolic Systems with Convolution Operators in Periodic Spaces. Matematičeskie zametki, Tome 82 (2007) no. 6, pp. 850-872. http://geodesic.mathdoc.fr/item/MZM_2007_82_6_a5/

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