Global in Space Regularity Results for the Heat Equation with Robin-Neumann Type Boundary Conditions in Time-varying Domains
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https://elib.sfu-kras.ru/handle/2311/110283Author:
Boudjeriou, Tahir
Kheloufi, Arezki
Буджериу, Тахир
Хелуфи, Арезки
Date:
2019-06Journal Name:
Журнал Сибирского федерального университета.Математика и физика.Journal of Siberian Federal University. Mathematics & Physics, 2019,Abstract:
This article deals with the heat equation
@tu @2x u = f in D; D = {(t; x) 2 R2 : a < t < b; (t) < x < +1}
with the function satisfying some conditions and the problem is supplemented with boundary conditions
of Robin-Neumann type. We study the global regularity problem in a suitable parabolic Sobolev space.
We prove in particular that for f 2 L2(D) there exists a unique solution u such that u; @tu; @jx
u 2 L2 (D) ; j = 1; 2: The proof is based on the domain decomposition method. This work complements the results obtained in [10]. Эта статья посвящена уравнению теплопроводности
@tu @2xu = f in D; D = {(t; x) 2 R2 : a < t < b; (t) < x < +1}
с функцией , удовлетворяющей некоторым условиям, и задача дополняется граничными условиями типа Робина-Неймана. Мы изучаем проблему глобальной регулярности в подходящем параболическом пространстве Соболева. Докажем, в частности, что для f 2 L2(D) существует
единственное решение u такое, что u; @tu; @jx
u 2 L2 (D) ; j = 1; 2. Доказательство основано на
методе декомпозиции области. Эта работа дополняет результаты, полученные в [10].
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