This paper is devoted to the homogenization of a semilinear parabolic equation with rapidly oscillating coefficients in a domain periodically perforated byε-periodic holes of size ε. A Neumann condition is prescribe...This paper is devoted to the homogenization of a semilinear parabolic equation with rapidly oscillating coefficients in a domain periodically perforated byε-periodic holes of size ε. A Neumann condition is prescribed on the boundary of the holes.The presence of the holes does not allow to prove a compactness of the solutions in L2. To overcome this difficulty, the authors introduce a suitable auxiliary linear problem to which a corrector result is applied. Then, the asymptotic behaviour of the semilinear problem as ε→ 0 is described, and the limit equation is given.展开更多
Analytical solutions are presented using method of separation of variables for the time periodic electroosmotic flow (EOF) of linear viscoelastic fluids in semicircular microchannel. The linear viscoelastic fluids use...Analytical solutions are presented using method of separation of variables for the time periodic electroosmotic flow (EOF) of linear viscoelastic fluids in semicircular microchannel. The linear viscoelastic fluids used here are described by the general Maxwell model. The solution involves analytically solving the linearized Poisson-Boltzmann (P -B) equation, together with the Cauchy momentum equation and the general Maxwell constitutive equation. By numerical computations, the influences of electric oscillating Reynolds number Re and Deborah number De on velocity amplitude are presented. For small Re, results show that the larger velocity amplitude is confined to the region near the charged wall when De is small. With the increase of the Deborah number De, the velocity far away the charged wall becomes larger for large Deborah number De. However, for larger Re, the oscillating characteristic of the velocity amplitude occurs and becomes significant with the increase of De, especially for larger Deborah number.展开更多
基金Project supported by the European Research and Training Network "HMS 2000" of the European Union under Contract HPRN-2000-00109.
文摘This paper is devoted to the homogenization of a semilinear parabolic equation with rapidly oscillating coefficients in a domain periodically perforated byε-periodic holes of size ε. A Neumann condition is prescribed on the boundary of the holes.The presence of the holes does not allow to prove a compactness of the solutions in L2. To overcome this difficulty, the authors introduce a suitable auxiliary linear problem to which a corrector result is applied. Then, the asymptotic behaviour of the semilinear problem as ε→ 0 is described, and the limit equation is given.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11062005, 11202092Opening Fund of State Key Laboratory of Nonlinear Mechanics, the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region+2 种基金the Natural Science Foundation of Inner Mongolia under Grant Nos.2010BS0107, 2012MS0107the Research Start up Fund for Excellent Talents at Inner Mongolia University under Grant No.Z20080211the Natural Science Key Fund of Inner Mongolia under Grant No.2009ZD01
文摘Analytical solutions are presented using method of separation of variables for the time periodic electroosmotic flow (EOF) of linear viscoelastic fluids in semicircular microchannel. The linear viscoelastic fluids used here are described by the general Maxwell model. The solution involves analytically solving the linearized Poisson-Boltzmann (P -B) equation, together with the Cauchy momentum equation and the general Maxwell constitutive equation. By numerical computations, the influences of electric oscillating Reynolds number Re and Deborah number De on velocity amplitude are presented. For small Re, results show that the larger velocity amplitude is confined to the region near the charged wall when De is small. With the increase of the Deborah number De, the velocity far away the charged wall becomes larger for large Deborah number De. However, for larger Re, the oscillating characteristic of the velocity amplitude occurs and becomes significant with the increase of De, especially for larger Deborah number.
