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91.
We consider the three-dimensional motion of a self-propelled deformable structure into a viscous incompressible fluid. The deformation of the solid is given whereas its position is unknown. Such a system could model the propulsion of fish-like swimmers. The equations of motion of the fluid are the Navier-Stokes equations and the equations for the structure are deduced from Newton’s laws. The corresponding system is a free boundary problem and the main result of the paper is the existence of weak solutions for this problem.  相似文献   
92.
We address the global persistence of analyticity and Gevrey-class regularity of solutions to the two and three-dimensional visco-elastic second-grade fluid equations. We obtain an explicit novel lower bound on the radius of analyticity of the solutions that does not vanish as t → ∞, and which is independent of the Rivlin–Ericksen material parameter α. Applications to the damped incompressible Euler equations are also given.  相似文献   
93.
94.
We study boundary value problems for the time-harmonic form of the Maxwell equations, as well as for other related systems of equations, on arbitrary Lipschitz domains in the three-dimensional Euclidean space. The main goal is to develop the corresponding theory for Lp-integrable bounday data for optimal values of p’s. We also discuss a number of relevant applications in electromagnetic scattering.  相似文献   
95.
We identify the optimal range of coefficients s, p for which differential forms with coefficients in the Sobolev space Lps(Ω) admit natural Hodge decompositions in arbitrary two and three dimensional Lipschitz domains Ω. To cite this article: D. Mitrea, M. Mitrea, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 109–112  相似文献   
96.
We consider acoustic scattering problems described by the mixed boundary value problem for the scalar Helmholtz equation in the exterior of a 2D bounded domain or in the exterior of a crack. The boundary of the domain is assumed to have a finite set of corner points where the scattered wave may have singular behaviour. The paper is concerned with the sensitivity of the far‐field pattern with respect to small perturbations of the shape of the scatterer. Using a modification of the method of adjoint problems, we obtain an integral representation for the Gâteaux derivative which contains only boundary values of functions easily computable by standard BEM and which depends explicitly on the perturbation of the boundary. In some cases, we show the direct influence of the singularities of the solution on the sensitivity of the far‐field pattern. In this way, we generalize the domain sensitivity analysis developed earlier for smooth domains by Hettlich, Kirsch, Kress, Potthast and others. Finally, we show that the same approach can be applied to scattering from 3D domains with smooth edges. Copyright © 2002 John Wiley & Sons, Ltd.  相似文献   
97.
In this paper we study problems of Buffon type with multiple intersections for lattices of parallelograms and as body test a line segment.  相似文献   
98.
We introduce certain Sobolev-Besov spaces which are particularly well adapted for measuring the smoothness of data and solutions of mixed boundary value problems in Lipschitz domains. In particular, these are used to obtain sharp well-posedness results for the Poisson problem for the Laplacian with mixed boundary conditions on bounded Lipschitz domains which satisfy a suitable geometric condition introduced by R.Brown in (1994). In this context, we obtain results which generalize those by D.Jerison and C.Kenig (1995) as well as E.Fabes, O.Mendez and M.Mitrea (1998). Applications to Hodge theory and the regularity of Green operators are also presented.

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99.
The paper is devoted to the study of solutions to linear elliptic boundary value problems in domains depending smoothly on a small perturbation parameter. To this end we transform the boundary value problem onto a fixed reference domain and obtain a problem in a fixed domain but with differential operators depending on the perturbation parameter. Using the Fredholm property of the underlying operator we show the differentiability of the transformed solution under the assumption that the dimension of the kernel does not depend on the perturbation parameter. Furthermore, we obtain an explicit representation for the corresponding derivative.  相似文献   
100.
On an open interval we follow the paths of a Brownian motion which returns to a fixed point as soon as it reaches the boundary and restarts afresh indefinitely. We determine that two paths starting at different points either cannot collapse or they do so almost surely. The problem can be modelled as a spatially inhomogeneous random walk on a group and contrasts sharply with the higher dimensional case in that if two paths may collapse they do so almost surely.  相似文献   
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