Related papers: Geometric constraints on Ekman boundary layer solu…
For a given family of smooth closed curves $\gamma^1,...,\gamma^\alpha\subset\mathbb{R}^3$ we consider the problem of finding an elastic \emph{connected} compact surface $M$ with boundary $\gamma=\gamma^1\cup...\cup\gamma^\alpha$. This is…
We present a second-order algorithm for approximating solutions to nonlocal diffusive processes in reaction-diffusion equations. The numerical scheme relies on a quadrature method for the spatial discretization and a second-order…
We consider an elliptic-parabolic free boundary problem that models the fluid flow through a partially saturated porous medium. The free boundary arises as the interface separating the saturated and unsaturated regions. Our main goal is to…
We introduce an analytical model that describes the vertical structure of Ekman boundary layer flows coupled to the Monin-Obukhov Similarity Theory (MOST) surface layer representation, which is valid for conventionally neutral (CNBL) and…
We study an inhomogeneous Neumann boundary value problem for functions of least gradient on bounded domains in metric spaces that are equipped with a doubling measure and support a Poincar\'e inequality. We show that solutions exist under…
We consider the heat equation in a smooth bounded convex domain $\Omega \subset \mathbb{R}^2$ with nonlinear Neumann boundary condition $\partial_\nu u = \lambda (u - u^3)$. Stable non-constant stationary solutions do not exist when…
We investigate in this paper the existence of the leading profile of a WKB expansion for quasilinear initial boundary value problems with a highly oscillating forcing boundary term. The framework is weakly nonlinear, as the boundary term is…
Axisymmetric boundary layers are studied using integral analysis of the governing equations for axial flow over a circular cylinder. The analysis includes the effect of pressure gradient and focuses on the effect of transverse curvature on…
Ekman pumping is a phenomenon induced by no-slip boundary conditions in rotating fluids. In the context of Rayleigh-B\'enard convection, Ekman pumping causes a significant change in the linear stability of the system compared to when it is…
We discuss the initial boundary value problem for a heat equation in a domain surrounded by a layer. The main features of this problem are twofold: on one hand, the layer is thin compared to the scale of the domain, and on the other hand,…
Irregular terrain has a pronounced effect on the propagation of seismic and acoustic wavefields but is not straightforwardly reconciled with structured finite-difference (FD) methods used to model such phenomena. Methods currently detailed…
This paper studies the behavior of singularly perturbed nonlinear differential equations with boundary-layer solutions that do not necessarily converge to an equilibrium. Using the average of the fast variable and assuming the boundary…
This paper is concerned with the homogenization of Dirichlet problem of elliptic systems in a bounded, smooth domain of finite type. Both the coefficients of the elliptic operator and the Dirichlet boundary data are assumed to be periodic…
The paper concerns boundary value problems for general nonautonomous first order quasilinear hyperbolic systems in a strip. We construct small global classical solutions, assuming that the right hand sides are small. In the case that all…
Extending investigations of Yarahmadian and Zumbrun in the strictly parabolic case, we study time-asymptotic stability of arbitrary (possibly large) amplitude noncharacteristic boundary layers of a class of hyperbolic-parabolic systems…
We introduce a new type of boundary conditions, {\it smooth boundary conditions}, for numerical studies of quantum lattice systems. In a number of circumstances, these boundary conditions have substantially smaller finite-size effects than…
We study global regularity for solutions of quasilinear elliptic equations of the form $\div \A(x,u,\nabla u) = \div \F $ in rough domains $\Omega$ in $\R^n$ with nonhomogeneous Dirichlet boundary condition. The vector field $\A$ is assumed…
We show that Busemann functions on a smooth, non-compact, complete, boundaryless, connected Riemannian manifold are viscosity solutions with respect to the Hamilton-Jacobi equation determined by the Riemannian metric and consequently they…
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…
A primitive problem of predicting the effective properties of composites is open boundary conditions. In this paper, Eshelby's transformation field method is developed to solve the open boundary problem of two-phase composites having…