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

Voir la notice de l'article provenant de la source Math-Net.Ru

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 
@article{MZM_2007_82_6_a5,
     author = {V. A. Litovchenko},
     title = {Cauchy {Problem} for {Parabolic} {Systems} with {Convolution} {Operators} in {Periodic} {Spaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {850--872},
     publisher = {mathdoc},
     volume = {82},
     number = {6},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_6_a5/}
}
TY  - JOUR
AU  - V. A. Litovchenko
TI  - Cauchy Problem for Parabolic Systems with Convolution Operators in Periodic Spaces
JO  - Matematičeskie zametki
PY  - 2007
SP  - 850
EP  - 872
VL  - 82
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2007_82_6_a5/
LA  - ru
ID  - MZM_2007_82_6_a5
ER  - 
%0 Journal Article
%A V. A. Litovchenko
%T Cauchy Problem for Parabolic Systems with Convolution Operators in Periodic Spaces
%J Matematičeskie zametki
%D 2007
%P 850-872
%V 82
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2007_82_6_a5/
%G ru
%F MZM_2007_82_6_a5
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/