scholarly journals Quantitative homogenization of the disordered $\nabla \phi $ model

2019 ◽  
Vol 24 (0) ◽  
Author(s):  
Paul Dario
Keyword(s):  
Quantitative Homogenization

scholarly journals Quantitative Homogenization of Attractors of Non-Newtonian Filtration Equations

2010 ◽  
Vol 2010 ◽  
pp. 1-25
Author(s):  
Emil Novruzov
Keyword(s):  
Fractional Order ◽  
A Priori ◽  
A Priori Estimate ◽  
Global Attractors ◽  
Explicit Estimate ◽  
Priori Estimate ◽  
Filtration Equation ◽  
Quantitative Homogenization

For a rapidly spatially oscillating nonlinearity we compare solutions of non-Newtonian filtration equation with solutions of the homogenized, spatially averaged equation . Based on an -independent a priori estimate, we prove that uniformly for all . Besides, we give explicit estimate for the distance between the nonhomogenized and the homogenized attractors in terms of the parameter ; precisely, we show fractional-order semicontinuity of the global attractors for .

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