scholarly journals A Compactness Result for the Sobolev Embedding via Potential Theory

2021 ◽  
pp. 61-91
Author(s):  
Filippo Camellini ◽  
Michela Eleuteri ◽  
Sergio Polidoro
Keyword(s):  
Potential Theory ◽  
Sobolev Embedding ◽  
Compactness Result

scholarly journals On 3D DDFV Discretization of Gradient and Divergence Operators: Discrete Functional Analysis Tools and Applications to Degenerate Parabolic Problems

2013 ◽  
Vol 13 (4) ◽  
pp. 369-410 ◽  
Author(s):  
Boris Andreianov ◽  
Mostafa Bendahmane ◽  
Florence Hubert
Keyword(s):  
Functional Analysis ◽  
Finite Volume ◽  
Parabolic Problems ◽  
Sobolev Embedding ◽  
Finite Volume Schemes ◽  
Compactness Result ◽  
Nonlinear Elliptic ◽  
Analysis Tools ◽  
Consistency Results ◽  
Discrete Compactness

Abstract. We present a detailed survey of discrete functional analysis tools (consistency results, Poincaré and Sobolev embedding inequalities, discrete W1,p compactness, discrete compactness in space and in time) for the so-called Discrete Duality Finite Volume (DDFV) schemes in three space dimensions. We concentrate mainly on the 3D CeVe-DDFV scheme presented in [IMA J. Numer. Anal., 32 (2012), pp. 1574–1603]. Some of our results are new, such as a general time-compactness result based upon the idea of Kruzhkov (1969); others generalize the ideas known for the 2D DDFV schemes or for traditional two-point-flux finite volume schemes. We illustrate the use of these tools by studying convergence of discretizations of nonlinear elliptic-parabolic problems of Leray–Lions kind, and provide numerical results for this example.

Potential Theory and Right Processes

2004 ◽  
Author(s):  
Lucian Beznea ◽  
Nicu Boboc
Keyword(s):  
Potential Theory

Sorption of phenols on hexadecyltrimethylammonium- modified bentonite: Application of Polanyi−Manes potential theory

2020 ◽  
pp. 0958305X2097728
Author(s):  
Jiyeon Choi ◽  
Dong-Ik Slong ◽  
Won Sik Shin
Keyword(s):  
Molar Volume ◽  
Potential Theory ◽  
Characteristic Curve ◽  
Chemical Compositions ◽  
Pore Filling ◽  
Sorption Data ◽  
Similar Chemical ◽  
Competitive Model ◽  
Sorption Potential ◽  
Sorption Systems

This study investigated the sorption of phenol and 4-chlorophenol (4-CP) on natural bentonite modified with hexadecyltrimethylammonium (HDTMA) cation. The Freundlich, Langmuir, Dubinin−Radushkevich (DR), Sips, and Polanyi−Dubinin−Manes (PDM) models fitted the sorption data well (R2 > 0.92). The Freundlich coefficient and the maximum sorbed amount of the Langmuir and PDM models of 4-CP were higher than phenol because of higher hydrophobicity (log Kow = 2.39 for 4-CP and 1.46 for phenol). The PDM model that includes solubility and molar volume was highly useful in predicting the sorption of phenols having widely different hydrophobicity and solubility. The characteristic curves, the plot of sorbed volume ( qv) versus the sorption potential per molar volume ( ε/ Vm) of 4-CP and phenol were distinctly different although they have similar chemical compositions. The selectivity of 4-CP (3.72) was higher than that of phenol (0.27) in binary sorption systems. The sorbed volume ( qv) in the binary sorption was remarkably reduced and the characteristic curve had wider distribution owing to competition in pore-filling. The sorption behaviors were elucidated by partitioning and pore-filling mechanisms. Among the tested binary sorption models, the modified Langmuir competitive model was the best in the prediction of the binary sorption (R2 > 0.98).

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