Asymptotic Solutions of the Wave Equation with Degenerate Velocity and with Right-Hand Side Localized in Space and Time
DOI:
https://doi.org/10.15407/mag14.04.393Анотація
Вивчається задача Коші для неоднорідного двовимірного хвильового рівняння зі змінними коефіцієнтами та нульовими початковими даними. Вважається, що права частина локалізована в просторі та часі. Рівняння розглядається в області з межею (берегом). Вважається, що швидкість на березі зникає як квадратний корінь відстані до берега, тобто хвильове рівняння має задану на кривій особливість. Ця крива і визначає межу області, в якій вивчається задача. Основний результат роботи – ефективні асимптотичні формули для розв'язку зазначеної задачі, включаючи окіл берега.
Mathematics Subject Classification: 34E20, 35L05, 35Q35.
Ключові слова:
хвильове рівняння, асимптотичний розв'язок, канонічний оператор Маслова.Посилання
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