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We define and prove the existence of unique solutions of an asymptotic Plateau problem for spacelike maximal surfaces in the pseudo-hyperbolic space of signature (2, n): the boundary data is given by loops on the boundary at infinity of the…
We introduce in this document a direct method allowing to solve numerically inverse type problems for linear hyperbolic equations. We first consider the reconstruction of the full solution of the wave equation posed in $\Omega\times (0,T)$…
In this paper, we are concerned with the two-dimensional steady supersonic combustion flows with a contact discontinuity moving through a nozzle of finite length. Mathematically, it can be formulated as a free boundary value problem…
For $\lambda \in (1/2, 1)$ and $\alpha$, we consider sets of numbers $x$ such that for infinitely many $n$, $x$ is $2^{-\alpha n}$-close to some $\sum_{i=1}^n \omega_i \lambda^i$, where $\omega_i \in \{0,1\}$. These sets are in Falconer's…
We prove that the sublevel set $\big\{z\in\mathbb D\colon k_{\mathbb D}\big(z,z_0\big)-k_{\mathbb D}\big(f(z),w_0\big)<\mu\big\}$, ${\mu\in\mathbb R}$, is geodesically convex with respect to the Poincar\'e distance $k_{\mathbb D}$ in the…
In this paper, we establish the convergence of solutions to the viscous Hamilton-Jacobi equation (with a Tonelli Hamiltonian): \[ \lambda u +H(x, du)=\varepsilon(\lambda)\Delta u,\quad \lambda>0 \] as $\lambda\rightarrow 0_+$, once the…
We examine a system of three-bosons confined to two dimensions in the presence of a perpendicular magnetic field within the framework of the adiabatic hyperspherical method. For the case of zero-range, regularized pseudo-potential…
In this paper, a few dual least-squares finite element methods and their application to scalar linear hyperbolic problems are studied. The purpose is to obtain $L^2$-norm approximations on finite element spaces of the exact solutions to…
The Hot Spots constant for bounded smooth domains was recently introduced by Steinerberger (2021) as a means to control the global extrema of the first nontrivial eigenfunction of the Neumann Laplacian by its boundary extrema. We generalize…
In this paper we consider scalar parabolic equations in a general non-smooth setting with emphasis on mixed interface and boundary conditions. In particular, we allow for dynamics and diffusion on a Lipschitz interface and on the boundary,…
We provide a detailed analysis of the boundary layers for mixed hyperbolic-parabolic systems in one space dimension and small amplitude regimes. As an application of our results, we describe the solution of the so-called boundary Riemann…
We prove the well--posedness of a dynamical perfect plasticity model under general assumptions on the stress constraint set and on the reference configuration. The problem is studied by combining both calculus of variations and hyperbolic…
The Cauchy problem for a quasilinear system of hyperbolic-parabolic equations is addressed with the method of linearization and fixed point. Coupling between the hyperbolic and parabolic variables is allowed in the linearization and we do…
We obtain an improved pseudolocality result for Ricci flows on two-dimensional surfaces that are initially almost-hyperbolic on large hyperbolic balls. We prove that, at the central point of the hyperbolic ball, the Gauss curvature remains…
Let $f$ be an $L^2$-normalized Hecke--Maass cuspidal newform of level $N$, character $\chi$ and Laplace eigenvalue $\lambda$. Let $N_1$ denote the smallest integer such that $N|N_1^2$ and $N_0$ denote the largest integer such that $N_0^2…
We study how good a lexicographically maximal solution is in the weighted matching and matroid intersection problems. A solution is lexicographically maximal if it takes as many heaviest elements as possible, and subject to this, it takes…
In the optimal partial transport problem, one is asked to transport a fraction $0<m \leq \min\{||f||_{L^1}, ||g||_{L^1}\}$ of the mass of $f=f \chi_\Omega$ onto $g=g\chi_\Lambda$ while minimizing a transportation cost. If $f$ and $g$ are…
In this paper we study the common distance between points and the behavior of a constant length step discrete random walk on finite area hyperbolic surfaces. We show that if the second smallest eigenvalue of the Laplacian is at least 1/4,…
Given a finite set, $A \subseteq \mathbb{R}^2$, and a subset, $B \subseteq A$, the \emph{MST-ratio} is the combined length of the minimum spanning trees of $B$ and $A \setminus B$ divided by the length of the minimum spanning tree of $A$.…
This paper is concerned with the optimal control problem governed by a linear parabolic equation and subjected to box constraints on control variables. This type of problem has important applications in heating and cooling systems. By…