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Analyzing complex fluid flow problems that involve multiple coupled domains, each with their respective set of governing equations, is not a trivial undertaking. Even more complicated is the elaborate and tedious task of specifying the…

Methods to solve the relativistic hydrodynamic equations are a key computational kernel in a large number of astrophysics simulations and are crucial to understanding the electromagnetic signals that originate from the merger of…

The nonlinear convection terms in the governing equations of compressible fluid flows are hyperbolic in nature and are nontrivial for modelling and numerical simulation. Many numerical methods have been developed in the last few decades for…

This paper addresses the numerical computation of critical angles between two convex cones in finite-dimensional Euclidean spaces. We present a novel approach to computing these critical angles by reducing the problem to finding stationary…

Based on the well-posedness of the stationary Wigner equation with inflow boundary conditions given in (A. Arnold, H et al. J. Math. Phys., 41, 2000), we prove without any additional prerequisite conditions that the solution of the Wigner…

We study the classical problem of planar shock refraction at an oblique density discontinuity, separating two gases at rest. When the shock impinges on the density discontinuity, it refracts and in the hydrodynamical case 3 signals arise.…

Recent control trends are increasingly relying on communication networks and wireless channels to close the loop for Internet-of-Things applications. Traditionally these approaches are model-based, i.e., assuming a network or channel model…

We present a rigorous approach and related techniques to construct global solutions of the 2-D Riemann problem with four-shock interactions for the Euler equations for potential flow. With the introduction of three critical angles: the…

We consider the elliptic estimates for Dirichlet-Neumann operator related to the water-wave problem on a two-dimensional corner domain in this paper. Due to the singularity of the boundary, there will be singular parts in the solution of…

A recently introduced two-phase flow model by Chun Shen is studied in this work. The model is derived to describe the dynamics of immersed water bubbles in liquid water as carrier. Several assumptions are made to obtain a reduced form of…

We examine the classical joint source--channel coding problem from the viewpoint of statistical physics and demonstrate that in the random coding regime, the posterior probability distribution of the source given the channel output is…

The interface problem for the linear Schr\"odinger equation in one-dimensional piecewise homogeneous domains is examined by providing an explicit solution in each domain. The location of the interfaces is known and the continuity of the…

We study formulations of bound state (Bethe-Salpeter) equations on arbitrary Riemannian manifolds. We obtain a hierarchy of equations for multipartice wave functions. These equations, at each number of particles, depend on certain choices…

We find an explicit form of entropy solutions to a Riemann problem for a degenerate nonlinear parabolic equation with piecewise constant velocity and diffusion coefficients. It is demonstrated that this solution corresponds to the minimum…

We prove a one-dimensional symmetry result for a weighted Dirichlet-to-Neumann problem arising in a model for water waves in dimension 3. More precisely we prove that minimizers and bounded monotone solutions depend on only one Euclidean…

We prove that a class of superlinear indefinite problems with homogeneous Neumann boundary conditions admits an arbitrarily high number of positive solutions, provided that the parameters of the problem are adequately chosen. The…

This paper is devoted to Riemann-Hilbert problems with constraints. We obtain results characterizing the existence of solutions as well as the dimension of the solution space in terms of certain indices. As an application, we show how such…

This note aims at demonstrating the advantage of moving-water well-balanced schemes over still-water well-balanced schemes for the shallow water equations. We concentrate on numerical examples with solutions near a moving-water equilibrium.…

A new algorithm for time dependent Hamilton Jacobi equations on networks, based on semi Lagrangian scheme, is proposed. It is based on the definition of viscosity solution for this kind of problems recently given in. A thorough convergence…

We study the wave equation on a bounded domain of $\mathbb R^m$ and on a compact Riemannian manifold $M$ with boundary. We assume that the coefficients of the wave equation are unknown but that we are given the hyperbolic…