| 1. |
- Chechkin, Gregory, et al.
(författare)
-
A new weighted Friedrichs-type inequality for a perforated domain with a sharp constant
- 2011
-
Ingår i: Eurasian Mathematical Journal. - 2077-9879. ; 2:1, s. 81-103
-
Tidskriftsartikel (refereegranskat)abstract
- We derive a new three-dimensional Hardy-type inequality for a cube for the class of functions from the Sobolev space $H^1$ having zero trace on small holes distributed periodically along the boundary. The proof is based on a careful analysis of the asymptotic expansion of the first eigenvalue of a related spectral problem and the best constant of the corresponding Friedrichs-type inequality.
|
|
| 2. |
|
|
| 3. |
|
|
| 4. |
|
|
| 5. |
- Chechkin, Gregory, et al.
(författare)
-
On spectrum of the Laplacian in a circle perforated along the boundary : Application to a Friedrichs-type inequality
- 2011
-
Ingår i: International Journal of Differential Equations. - : Hindawi Limited. - 1687-9643 .- 1687-9651. ; 2011
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper we construct and verify the asymptotic expansion for the spectrum of a boundary-value problem in a unit circle periodically perforated along the boundary. It is assumed that the size of perforation and the distance to the boundary of the circle are of the same smallness. As an application of the obtained results the asymptotic behavior of the best constant in a Friedrichs-type inequality is investigated.
|
|
| 6. |
- Fabricius, John, et al.
(författare)
-
A rigorous derivation of the time-dependent Reynolds equation
- 2013
-
Ingår i: Asymptotic Analysis. - 0921-7134 .- 1875-8576. ; 84:1-2, s. 103-121
-
Tidskriftsartikel (refereegranskat)abstract
- We study the asymptotic behavior of solutions of the evolution Stokes equation in a thin three-dimensional domain bounded by two moving surfaces in the limit as the distance between the surfaces approaches zero. Using only a priori estimates and compactness it is rigorously verified that the limit velocity field and pressure are governed by the time-dependent Reynolds equation.
|
|
| 7. |
- Fabricius, John, et al.
(författare)
-
Asymptotic behaviour of Stokes flow in a thin domain with amoving rough boundary
- 2014
-
Ingår i: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences. - : The Royal Society. - 1364-5021 .- 1471-2946. ; 470:2167
-
Tidskriftsartikel (refereegranskat)abstract
- We consider a problem that models fluid flow in a thin domain bounded by two surfaces. One of the surfaces is rough and moving, whereas the other is flat and stationary. The problem involves two small parameters ε and μ that describe film thickness and roughness wavelength, respectively. Depending on the ratio λ = ε/μ, three different flow regimes are obtained in the limit as both of them tend to zero. Time-dependent equations of Reynolds type are obtained in all three cases (Stokes roughness, Reynolds roughness and high-frequency roughness regime). The derivations of the limiting equations are based on formal expansions in the parameters ε and μ.
|
|
| 8. |
|
|
| 9. |
|
|
| 10. |
|
|
