Asymptotic Solutions of the Wave Equation with Degenerate Velocity and with Right-Hand Side Localized in Space and Time

We study the Cauchy problem for the inhomogeneous two-dimensional wave equation with variable coefficients and zero initial data. The righthand side is assumed to be localized in space and time. The equation is considered in a domain with a boundary (shore). The velocity is assumed to vanish on the...

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Збережено в:
Бібліографічні деталі
Дата:2018
Автори: Anikin, A., Dobrokhotov, S., Nazaikinskii, V.
Формат: Стаття
Мова:English
Опубліковано: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2018
Назва видання:Журнал математической физики, анализа, геометрии
Онлайн доступ:http://dspace.nbuv.gov.ua/handle/123456789/145880
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Asymptotic Solutions of the Wave Equation with Degenerate Velocity and with Right-Hand Side Localized in Space and Time / A. Anikin, S. Dobrokhotov, V. Nazaikinskii // Журнал математической физики, анализа, геометрии. — 2018. — Т. 14, № 4. — С. 393-405. — Бібліогр.: 30 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
Опис
Резюме:We study the Cauchy problem for the inhomogeneous two-dimensional wave equation with variable coefficients and zero initial data. The righthand side is assumed to be localized in space and time. The equation is considered in a domain with a boundary (shore). The velocity is assumed to vanish on the shore as a square root of the distance to the shore, that is, the wave equation has a singularity on the curve. This curve determines the boundary of the domain where the problem is studied. The main result of the paper is efficient asymptotic formulas for the solution of this problem, including the neighborhood of the shore.