# Well-posedness results for the wave equation generated by the Bessel operator

 dc.contributor.author Bekbolat, B. dc.contributor.author Tokmagambetov, N. dc.date.accessioned 2021-09-30T09:02:28Z dc.date.available 2021-09-30T09:02:28Z dc.date.issued 2021-03-30 dc.identifier.citation Bekbolat B. Well-posedness results for the wave equation generated by the Bessel operator/B. Bekbolat, N. Tokmagambetov//Қарағанды университетінің хабаршысы. Математика сериясы.= Вестник Карагандинского университета. Серия Математика. = Bulletin of the Karaganda University. Mathematics Series. -2021. №1. Р.11-16. ru_RU dc.identifier.uri http://rep.ksu.kz/xmlui/handle/data/11139 dc.description.abstract In this paper, we consider the non-homogeneous wave equation generated by the Bessel operator. We prove ru_RU the existence and uniqueness of the solution of the non-homogeneous wave equation generated by the Bessel operator. The representation of the solution is given. We obtained a priori estimates in Sobolev type space. This problem was firstly considered in the work of M. Assal [1] in the setting of Bessel-Kingman hypergroups. The technique used in [1] is based on the convolution theorem and related estimates. Here, we use a different approach. We study the problem from the point of the Sobolev spaces. Namely, the conventional Hankel transform and Parseval formula are widely applied by taking into account that between the Hankel transformation and the Bessel differential operator there is a commutation formula [2]. dc.language.iso en ru_RU dc.publisher KU Publ. ru_RU dc.relation.ispartofseries Қарағанды университетінің хабаршысы. Математика сериясы.= Вестник Карагандинского университета. Серия Математика. = Bulletin of the Karaganda University. Mathematics Series.;№1(101)/2021 dc.subject Bessel operator ru_RU dc.subject wave equation ru_RU dc.subject Hankel transform ru_RU dc.subject inverse Hankel transform ru_RU dc.subject Sobolev type space ru_RU dc.title Well-posedness results for the wave equation generated by the Bessel operator ru_RU dc.title.alternative Бессель операторы арқылы туындаған толқын теңдеуі үшін тұрақтылық нәтижелері ru_RU dc.title.alternative Результаты корректности волнового управления, порожденного оператором Бесселя ru_RU dc.type Article ru_RU
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