Geodesic
Semigroup Classification and Gelfand--Shilov Classification of Systems of Partial Differential Equations
Matematičeskie zametki, Tome 104 (2018) no. 6, pp. 895-911.

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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. 
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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/

[1] I. V. Melnikova, A. I. Filinkov, U. A. Anufrieva, “Abstract stochastic equations. I. Classical and distributional solutions”, J. Math. Sci. (New York), 111:2 (2002), 3430–3475 | MR | Zbl

[2] I. V. Melnikova, Stochastic Cauchy Problems in Infinite Dimensions. Regularized and Generalized Solutions, CRC Press, Boca Raton, FL, 2016 | MR | Zbl

[3] I. M. Gelfand, G. E. Shilov, Obobschennye funktsii. Vyp. 3. Nekotorye voprosy teorii differentsialnykh uravnenii, Fizmatgiz, M., 1958 | MR | Zbl

[4] U. A. Anufrieva, I. V. Melnikova, “Osobennosti i regulyarizatsiya nekorrektnykh zadach Koshi s differentsialnymi operatorami”, Differentsialnye uravneniya i teoriya polugrupp, SMFN, 14, RUDN, M., 2005, 3–156 | MR | Zbl

[5] K.-J. Engel, R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Springer-Verlag, Berlin, 1999 | MR | Zbl

[6] W. Arendt, Ch. J. K. Batty, M. Hieber, F. Neubrander, Vector-Valued Laplace Transform and Cauchy Problems, Birkhäuser Verlag, Basel, 2001 | MR

[7] I. V. Melnikova, A. Filinkov, The Cauchy Problem: Three Approaches, Chapman Hall/CRC Monogr. Surv. Pure Appl. Math., 120, Chapman Hall/CRC, Boca Raton, FL, 2001 | MR

[8] H. O. Fattorini, The Cauchy Problem, Addison-Wesley Publ., Reading, MA, 1983 | MR

[9] I. Cioranescu, “Local convoluted semigroups”, Lecture Notes in Pure and Appl. Math., 168, Marcel Dekker, New York, 1995, 107–122 | MR

[10] I. V. Melnikova, U. A. Alekseeva, “Weak regularized solutions to stochastic Cauchy problems”, CMSIM J., 2014, no. 1, 49–56

[11] J. Chazarain, “Problèmes de Cauchy abstraits et applications à quelques problèmes mixtes”, J. Funct. Anal., 7:3 (1971), 386–446 | DOI | MR | Zbl

[12] H. Komatsu, “Ultradistributions. I. Structure theorems and a characterization”, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 20:1 (1973), 25–106 | MR | Zbl