弱多孔介质中具有卷积的均匀化问题的可解性

G. Sandrakov, A. Hulianytskyi
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引用次数: 1

摘要

研究了弱多孔介质中扩散和过滤的非平稳方程的初边值问题。给出了这类问题的可解性以及相应的带卷积的齐次化问题的断言。这些表述在一般初始数据和非齐次初始条件下得到了证明,是热方程初边值问题可解性的经典结果的推广。证明使用了先验估计方法和著名的Agranovich-Vishik方法,该方法用于研究一般类型的抛物问题。
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SOLVABILITY OF HOMOGENIZED PROBLEMS WITH CONVOLUTIONS FOR WEAKLY POROUS MEDIA
Initial boundary value problems for nonstationary equations of diffusion and filtration in weakly porous media are considered. Assertions about the solvability of such problems and the corresponding homogenized problems with convolutions are given. These statements are proved for general initial data and inhomogeneous initial conditions and are generalizations of classical results on the solvability of initial-boundary value problems for the heat equation. The proofs use the methods of a priori estimates and the well-known Agranovich–Vishik method, developed to study parabolic problems of general type.
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