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Title: The Darboux Problem for a Class of 3-D Weakly Hyperbolic Equations
Other Titles: Задача на дарбу за клас тримерни слабо хиперболични уравнения
Authors: Popivanov, Nedyu
Hristov, Tsvetan
Keywords: Weakly Hyperbolic Equations
Boundary Value Problems
Generalized Solutions
Quasi-Regular Solutions
Singular Solutions
Issue Date: 2011
Publisher: Union of Bulgarian Mathematicians
Citation: Union of Bulgarian Mathematicians, Vol. 40, No 1, (2011), 193p-199p
Abstract: Some three-dimensional analogues of the plane Darboux problems for weakly hyperbolic equations are studied. In 1952 M. Protter formulated new 3-D boundary value problems for a class of weakly hyperbolic equations, as well as for some hyperbolic- elliptic equations. In the contrast of the well-posedness of the Darboux problem in 2-D case, the new problems are strongly ill-posed. For weakly hyperbolic equation, involving lower order terms, we find sufficient conditions for existence and uniqueness of generalized solutions with isolated power-type singularities as well as for uniqueness of quasi-regular solutions to the Protter problem. *2000 Mathematics Subject Classification: 35L20, 35A20.
Description: Недю Попиванов, Цветан Христов - Изследвани са някои тримерни аналози на задачата на Дарбу в равнината. През 1952 М. Протер формулира нови тримерни гранични задачи както за клас слабо хиперболични уравнения, така и за някои хиперболично-елиптични уравнения. За разлика от коректността на двумерната задача на Дарбу, новите задачи са некоректни. За слабо хиперболични уравнения, съдържащи младши членове, ние намираме достатъчни условия както за съществуване и единственост на обобщени решения с изолирана степенна особеност, така и за единственост на квази-регулярни решения на задачата на Протер.
ISBN: 1313-3330
Appears in Collections:Union of Bulgarian Mathematicians 2011

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