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Numerical Analysis of the Closed Osmometer Problem
Author(s) -
Frischmuth K.,
Hänler M.
Publication year - 1999
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/(sici)1521-4001(199902)79:2<107::aid-zamm107>3.0.co;2-e
Subject(s) - osmometer , discretization , mathematics , boundary value problem , constructive , domain (mathematical analysis) , ode , mathematical analysis , numerical analysis , computer science , chemistry , organic chemistry , process (computing) , operating system
The closed osmometer problem, formulated by Rubinstein and studied by Rubinstein and Martuzans [5], is solved analytically and numerically. The model consists of a diffusion equation on an unknown domain and an equation describing the motion of a membrane that constitutes the boundary of the domain. In particular, the 1D case is studied where the second equation reduces to an ODE which expresses the equilibrium of osmotic and mechanical pressures. The initial‐boundary value problem for the model equations is shown to be well‐posed in appropriate spaces by a constructive technique. We compare results obtained by direct implementation of the iteration used in the proof with numerical solutions calculated by a semi‐discretization method.