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A class of pseudo‐parabolic equations: existence, uniqueness of weak solutions, and error estimates for the Euler‐implicit discretization
Author(s) -
Fan Y.,
Pop I.S.
Publication year - 2011
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1537
Subject(s) - uniqueness , mathematics , discretization , backward euler method , euler equations , class (philosophy) , euler's formula , mathematical analysis , discretization error , flow (mathematics) , geometry , computer science , artificial intelligence
In this paper, we investigate a class of pseudo‐parabolic equations. Such equations model two‐phase flow in porous media where dynamic effects are included in the capillary pressure. The existence and uniqueness of a weak solution are proved, and error estimates for an Euler implicit time discretization are obtained. Copyright © 2011 John Wiley & Sons, Ltd.