Related papers: The boundary layer problem in Bayesian adaptive qu…
This paper studies the boundary behaviour at mechanical equilibrium at the ends of a finite interval of a class of systems of interacting particles with monotone decreasing repulsive force. Our setting covers pile-ups of dislocations,…
Boundary integral equations are an efficient and accurate tool for the numerical solution of elliptic boundary value problems. The solution is expressed as a layer potential; however, the error in its evaluation grows large near the…
We propose a new class of layer-adapted meshes for weak boundary layers. Especially for fourth-order problems these meshes are extremely useful.
We study the boundary behavior of solutions to parabolic double-phase equations through the celebrated Wiener's sufficiency criterion. The analysis is conducted for cylindrical domains and the regularity up to the lateral boundary is shown…
The construction of Ekman boundary layer solutions near the non-flat boundaries presents a complex challenge, with limited research on this issue. In Masmoudi's pioneering work [Comm. Pure Appl. Math. 53 (2000), 432--483], the Ekman…
A compressible laminar boundary layer developing over an isotropic porous substrate is investigated by asymptotic and numerical methods. The substrate is modeled as an array of cubes. The momentum and enthalpy balance equations are derived…
We study the initial boundary value problem for a heat equation in a domain containing a thin layer. The thermal conductivity of the layer is drastically different from that of the bulk of the domain; moreover, the layer is anisotropic and…
Spatial process models are widely used for modeling point-referenced variables arising from diverse scientific domains. Analyzing the resulting random surface provides deeper insights into the nature of latent dependence within the studied…
In this paper, we study the well-posedness of boundary layer problems for the inhomogeneous incompressible magnetohydrodynamics(MHD) equations, which are derived from the two dimensional density-dependent incompressible MHD equations.Under…
Multi-element wings are popular in the aerospace community due to their high lift performance. Turbulent flow simulations of these configurations require very fine mesh spacings especially near the walls, thereby making use of a boundary…
We study the boundary of an affine invariant submanifold of a stratum of translation surfaces in a partial compactification consisting of all finite area Abelian differentials over nodal Riemann surfaces, modulo zero area components. The…
In this paper, we investigate the validity of boundary layer expansions for the MHD system in a rectangle. We describe the solution up to any order when the tangential magnetic field is much smaller or much larger than the tangential…
The present work deals with the resolution of the Poisson equation in a bounded domain made of a thin and periodic layer of finite length placed into a homogeneous medium. We provide and justify a high order asymptotic expansion which takes…
Absorbing layers are sometimes required to be impractically thick in order to offer an accurate approximation of an absorbing boundary condition for the Helmholtz equation in a heterogeneous medium. It is always possible to reduce an…
Convergence of the solutions of nonhomogeneous linear singularly perturbed systems to that of the corresponding reduced singular system on the half-line [0, $\infty $) is considered. To include the situation on a neighborhood of initial…
This article proves the well posedness of the boundary value problemthat arises when PML algorithms are applied to Pauli's equationswith a three dimensional rectangle as computational domain. The absorptionsare positive near the boundary…
We analyze an adaptive boundary element method for the weakly-singular and hypersingular integral equations for the 2D and 3D Helmholtz problem. The proposed adaptive algorithm is steered by a residual error estimator and does not rely on…
Grain boundaries in extremely confined colloidal smectics possess a topological fine structure with coexisting nematic and tetratic symmetry of the director field. An alternative way to approach the problem of smectic topology is via the…
We introduce a level set based approach to Bayesian geometric inverse problems. In these problems the interface between different domains is the key unknown, and is realized as the level set of a function. This function itself becomes the…
We investigate the incompressible and compressible heat conducting boundary layer with applying the two-dimensional self-similar Ansatz. Analytic solutions can be found for the incompressible case which can be expressed with special…