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Эта публикация цитируется в 4 научных статьях (всего в 4 статьях)
Maximal regularity estimates for higher order differential equations with fluctuating coefficients
K. N. Ospanov, Zh. B. Yeskabylova, D. R. Beisenova Department of Mechanics and Mathematics,
L.N. Gumilyov Eurasian National University,
13 Munaitpasov St.,
010008 Astana, Kazakhstan
Аннотация:
We give the well-posedness conditions in $L_2(-\infty,+\infty)$ for the following differential
equation
$$
-y'''+p(x)y'+q(x)y=f(x),
$$
where $p$ and $q$ are continuously differentiable and continuous functions, respectively, and $f\in L_2(R)$. Moreover, we prove for the solution y of this equation the following maximal regularity
estimate:
$$
||y'''||_2+||py'||_2+||qy||_2\leqslant C||f||_2
$$
(here $||\cdot||_2$ is the norm in $L_2(-\infty,+\infty)$). We assume that the intermediate coefficient $p$ is fast
oscillating and not controlled by the coefficient $q$. The sufficient conditions obtained by us are
close to necessary ones. We give similar results for the fourth-order differential equation with
singular intermediate coefficients.
Ключевые слова и фразы:
differential equation, oscillating coefficient, well-posedness, maximal regularity estimate.
Поступила в редакцию: 30.04.2018
Образец цитирования:
K. N. Ospanov, Zh. B. Yeskabylova, D. R. Beisenova, “Maximal regularity estimates for higher order differential equations with fluctuating coefficients”, Eurasian Math. J., 10:2 (2019), 65–74
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/emj330 https://www.mathnet.ru/rus/emj/v10/i2/p65
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Страница аннотации: | 207 | PDF полного текста: | 65 | Список литературы: | 14 |
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