Semigroup Classification and Gelfand--Shilov Classification of Systems of Partial Differential Equations

I. V. Mel'nikova; U. A. Alekseeva

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Semigroup Classification and Gelfand--Shilov Classification of Systems of Partial Differential Equations

I. V. Mel'nikova ; U. A. Alekseeva

Matematičeskie zametki, Tome 104 (2018) no. 6, pp. 895-911

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Résumé

Two approaches to systems of linear partial differential equations are considered: the traditional approach based on the generalized Fourier transform and the semigroup approach, under which the system is considered as a particular case of an operator-differential equation. For these systems, the semigroup classification and the Gelfand–Shilov classification are compared.

Keywords: semigroup of operators, system of partial differential equations, abstract Cauchy problem
Mots-clés : Fourier transform, distribution.

@article{MZM_2018_104_6_a7,
     author = {I. V. Mel'nikova and U. A. Alekseeva},
     title = {Semigroup {Classification} and {Gelfand--Shilov} {Classification} of {Systems} of {Partial} {Differential} {Equations}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {895--911},
     publisher = {mathdoc},
     volume = {104},
     number = {6},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_104_6_a7/}
}

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I. V. Mel'nikova; U. A. Alekseeva. Semigroup Classification and Gelfand--Shilov Classification of Systems of Partial Differential Equations. Matematičeskie zametki, Tome 104 (2018) no. 6, pp. 895-911. http://geodesic.mathdoc.fr/item/MZM_2018_104_6_a7/