Geodesic
The Cauchy problem for evolution equations with the Bessel operator of infinite order. II
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2010), pp. 31-42 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove the correct solvability of the Cauchy problem for singular evolution equations of infinite order in classes of initial conditions that are generalized functions like ultra-distributions (analytic functionals).
Keywords: Cauchy problem, Bessel operator of infinite order.
Mots-clés : evolution equation, distribution 
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V. V. Gorodestkii; O. V. Martynyuk. The Cauchy problem for evolution equations with the Bessel operator of infinite order. II. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2010), pp. 31-42. http://geodesic.mathdoc.fr/item/IVM_2010_7_a2/

[1] Gorodetskii V. V., Martynyuk O. V., “Zadacha Koshi dlya evolyutsionnykh uravnenii s operatorom Besselya beskonechnogo poryadka, I”, Izv. vuzov. Matematika, 2010, no. 6, 3–15

[2] Gurevich B. L., “Nekotorye prostranstva osnovnykh i obobschennykh funktsii i problema Koshi dlya konechno-raznostnykh sistem”, DAN SSSR, 99:6 (1954), 893–896

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

[4] Gelfand I. M., Shilov G. E., “Preobrazovaniya Fure bystro rastuschikh funktsii i voprosy edinstvennosti zadachi Koshi”, UMN, 8:6 (1953), 3–54 | MR | Zbl

[5] Zhitomirskii Ya. I., “Zadacha Koshi dlya sistem lineinykh uravnenii v chastnykh proizvodnykh s differentsialnym operatorom Besselya”, Matem. sb., 36(78):2 (1955), 299–310 | MR | Zbl

[6] Krekhivskii V. V., “Teoremy edinstvennosti reshenii zadachi Koshi dlya uravnenii s operatorom Besselya”, Matem. modelir. fiz. prots., In-t matematiki AN USSR, Kiev, 1989, 82–86 | MR

[7] Gelfand I. M., Shilov G. E., Prostranstva osnovnykh i obobschennykh funktsii, Fizmatgiz, M., 1958 | MR

[8] Matiichuk M. I., Parabolichni singulyarni kraiovi zadachi, Institut matematiki NAN Ukraïni, Kiïv, 1999