Related papers: On optimality and bounds for internal solutions ge…
The very weak solution of the Poisson equation with $L^2$ boundary data is defined by the method of transposition. The finite element solution with regularized boundary data converges in the $L^2(\Omega)$-norm with order $1/2$ in convex…
The accuracy of time-domain solutions of the inhomogeneous Teukolsky equation is improved significantly. Comparing energy fluxes in gravitational waves with highly accurate frequency-domain results for circular equatorial orbits in…
We apply the local discontinuous Galerkin (LDG for short) method to solve a mixed boundary value problems for the Helmholtz equation in bounded polygonal domain in 2D. Under some assumptions on regularity of the solution of an adjoint…
We aim at the development and analysis of the numerical schemes for approximately solving the backward diffusion-wave problem, which involves a fractional derivative in time with order $\alpha\in(1,2)$. From terminal observations at two…
In this paper we prove the existence of a time-frequency space that best approximates a given finite set of data. Here best approximation is in the least square sense, among all time-frequency spaces with no more than a prescribed number of…
This paper analyzes the reconstruction of diffusion and absorption parameters in an elliptic equation from knowledge of internal data. In the application of photo-acoustics, the internal data are the amount of thermal energy deposited by…
The Smoluchowski diffusion equation describes diffusion in the presence of external forces. Studying the mechanical response of soft materials to linear forces, such as shear, results in a boundary value problem involving an…
We study the well-posedness of the compressible boundary layer equations with data being analytic in the tangential variable of the boundary. The compressible boundary layer equations, a nonlinear coupled system of degenerate parabolic…
In this paper, we establish some local and global solutions for the two phase incompressible inhomogeneous flows with moving interfaces in $L_p-L_q$ maximal regularity class. Compared with previous results obtained by V.A.Solonnikov and by…
This paper is concerned with the mathematical analysis of the time-domain electromagnetic scattering problem in an infinite rectangular waveguide. A transparent boundary condition is developed to reformulate the problem into an equivalent…
We develop a unified nonparametric framework for sharp partial identification and inference on inequality indices when the data contain coarsened observations of the variable of interest. We characterize the extremal allocations for all…
This work proposes a novel variational approximation of partial differential equations on moving geometries determined by explicit boundary representations. The benefits of the proposed formulation are the ability to handle large…
A methodology is presented for bounding all higher moments of the local hydrostatic stress field inside random two phase linear thermoelastic media undergoing macroscopic thermomechanical loading. The method also provides a lower bound on…
The aim of this paper is to develop stable and accurate numerical schemes for boundary integral formulations of the heat equation with Dirichlet boundary conditions. The accuracy of Galerkin discretisations for the resulting boundary…
We propose an efficient semi-Lagrangian characteristic mapping method for solving the one+one-dimensional Vlasov-Poisson equations with high precision on a coarse grid. The flow map is evolved numerically and exponential resolution in…
Measurements on a subset of the boundary are common in electrical impedance tomography, especially any electrode model can be interpreted as a partial boundary problem. The information obtained is different to full-boundary measurements as…
We consider the inverse problem for the wave equation on a compact Riemannian manifold or on a bounded domain of $\R^n$, and generalize the concept of {\em domain of influence}. We present an efficient minimization algorithm to compute the…
We consider bounds on the convergence of Ritz values from a sequence of Krylov subspaces to interior eigenvalues of Hermitean matrices. These bounds are useful in regions of low spectral density, for example near voids in the spectrum, as…
The Feynman-Kac formula for the exterior-value problem for the fractional Laplacian leads to a walk-outside-spheres algorithm via sampling alpha-stable Levy processes on their exit from maximally inscribed balls and sampling their…
Time-frequency (TF) representations of time series are intrinsically subject to the boundary effects. As a result, the structures of signals that are highlighted by the representations are garbled when approaching the boundaries of the TF…