New singular solutions for the (3+1)-D Protter problem

Show simple item record Popov, T.P. 2019-03-04T11:12:48Z 2019-03-04T11:12:48Z 2018-09-29
dc.identifier.citation Popov, T.P. New singular solutions for the (3+1)-D Protter problem/ T.P.Popov//Қарағанды универисетінің хабаршысы. Математика сериясы.=Вестник Карагандинского университета. Серия Математика=Bulletin of the Karaganda University. Mathematics Series.-2018.- №3.-Р.61-68. ru_RU
dc.identifier.issn 2518-7929
dc.description.abstract For the nonhomogeneous wave equation with three space and one time variables we study a boundary value problem that can be regarded as a four-dimensional analogue of the Darboux problem in R2. Unlike the planar Darboux problem, the R4-version is not well posed and has an infinite-dimensional cokernel. Therefore the problem is not Fredholm in the framework of classical solvability. On the other hand, it is known that for smooth right-hand side functions, there is a uniquely determined generalized solution that may have a strong power-type singularity at one boundary point. The singularity is isolated at the vertex of the characteristic light cone and does not propagate along the cone. In the present article we announce new singular solutions with exponential growth. ru_RU
dc.language.iso other ru_RU
dc.publisher Ye.A.Buketov Karaganda State University Publ. ru_RU
dc.relation.ispartofseries Қарағанды универисетінің хабаршысы. МАТЕМАТИКА Сериясы.=Вестник Карагандинского университета. Серия МАТЕМАТИКА.=Bulletin of the Karaganda University. MATHEMATICS Series.;№ 3(91)/2018
dc.subject wave equation ru_RU
dc.subject boundary value problems ru_RU
dc.subject generalized solution ru_RU
dc.subject singular solutions ru_RU
dc.subject propagation of singularities ru_RU
dc.subject special functions ru_RU
dc.title New singular solutions for the (3+1)-D Protter problem ru_RU
dc.title.alternative Проттер (3+1)-D есебінің жаңа сингулярлық шешімдері ru_RU
dc.title.alternative Новые сингулярные решения для (3+1)-D задачи Проттера ru_RU
dc.type Article ru_RU

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