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Shape Sensitivity Analysis of the Dirichlet Laplacian in a Half-Space

100%
Amrouche C., Nečasová Š., Sokołowski J.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2004
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tom 52
|
nr 4
365-380
EN
Material and shape derivatives for solutions to the Dirichlet Laplacian in a half-space are derived by an application of the speed method. The proposed method is general and can be used for shape sensitivity analysis in unbounded domains for the Neumann Laplacian as well as for the elasticity boundary value problems.
2
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$L^q$-approach to weak solutions of the Oseen flow around a rotating body

100%
Kračmar S., Nečasová Š., Penel P.
Banach Center Publications
|
2008
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tom 81
|
nr 1
259-276
EN
We consider the time-periodic Oseen flow around a rotating body in ℝ³. We prove a priori estimates in $L^{q}$-spaces of weak solutions for the whole space problem under the assumption that the right-hand side has the divergence form. After a time-dependent change of coordinates the problem is reduced to a stationary Oseen equation with the additional term -(ω ∧ x)·∇u + ω ∧ u in the equation of momentum where ω denotes the angular velocity. We prove the existence of generalized weak solutions in $L^{q}$-space using Littlewood-Paley decomposition and maximal operators.
3
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Incompressible Maxwell-Boussinesq approximation: Existence, uniqueness and shape sensitivity

87%
Consiglieri L., Nečasová Š., Sokolowski J.
Control and Cybernetics
|
2009
|
tom 38
|
nr 4A
1193-1215
4
Content available remote

Shape differentiability of the Neumann problem of the Laplace equation in the half-space

87%
Amrouche C., Nečasová Š., Sokołowski J.
Control and Cybernetics
|
2008
|
tom 37
|
nr 4
747-769
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