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Roughness effect on Neumann boundary condition [PDF]

Asymptotic Analysis, 2012
We study the effect of a periodic roughness on a Neumann boundary condition. We show that, as in the case of a Dirichlet boundary condition, it is possible to approach this condition by a more complex law on a domain without rugosity, called wall law. This approach is however different from that usually used in Dirichlet case.
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Estimates of Heat Kernels with Neumann Boundary Conditions

Potential Analysis, 2012
This paper is concerned with two-sided estimates for the heat kernels corresponding to general elliptic operators of the form \(Lu=\frac{1}{2}\nabla\cdot(A\nabla u)+b\cdot \nabla u-\nabla(\hat bu)+qu\) in a bounded domain \(D\subset \mathbb R^N\) subject to Robin boundary conditions: \(\frac{1}{2}\langle A\nabla u,n\rangle-\langle \hat b,n\rangle u=0\)
Zhang, Tusheng, Yang, Xue
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Curvature sensors, adaptive optics, and Neumann boundary conditions

Applied Optics, 2001
We consider the Neumann boundary-value problem for curvature adaptive optics systems. We show that, because curvature sensors average over extended regions of the wave front, inconsistent data for the solution of the Neumann problem result when the measurements are treated as local.
C, Ftaclas, A, Kostinski
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Differaction for a neumann boundary condition

Communications in Partial Differential Equations, 1997
Let be a bounded open set in Rn and P be a constant coefficient operator of order 2 in Rn X Rt such that admits a strictly diffractive point. We calculate in this paper the principal symbol of the operatorK& transforming for a solution in the neighborhood of a strictly diffractive point We deduce from this calculation the principal symbol of the wave ...
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Neumann, Fourier and Mixed Boundary Conditions

2018
The GDM and its analysis are adapted here to cope with Neumann, Fourier and mixed boundary conditions. Properties of trace operators are detailed.
Jérôme Droniou, Robert Eymard, Thierry Gallouët, Cindy Guichard, Raphaèle Herbin   +4 more
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Small sets for Neumann boundary conditions

Mathematische Nachrichten, 2008
AbstractFor an open set D ⊆ ℝn and a relatively closed subset E ⊆ D of Lebesgue measure zero, we investigate conditions for the property that Brownian motion with reflexion at the boundary on D and D \ E are the same. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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Decomposition Solutions for Neumann Boundary Conditions

1994
For simplicity, consider a linear differential equation Lu + Ru = g where L = d2/dx2 (and R can involve no differentiations higher than first-order).
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Integral Method of Boundary Characteristics: Neumann Condition

Journal of Engineering Physics and Thermophysics, 2018
A new algorithm, based on systems of identical equalities with integral and differential boundary characteristics, is proposed for solving boundary-value problems on the heat conduction in bodies canonical in shape at a Neumann boundary condition. Results of a numerical analysis of the accuracy of solving heat-conduction problems with variable boundary
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Nonlinear Elliptic Equations with Neumann Boundary Conditions

2013
This chapter aims to present relevant knowledge regarding recent progress on nonlinear elliptic equations with Neumann boundary conditions. In fact, all the results presented here bring novelties with respect to the available literature. We emphasize the specific functional setting and techniques involved in handling the Neumann problems, which are ...
Dumitru Motreanu, Viorica Venera Motreanu, Nikolaos Papageorgiou   +2 more
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Neumann and Robin boundary conditions

2022
Wolfgang Arendt, Karsten Urban
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