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In this paper, we are concerned with the non-relativistic limit of a class of computable approximation models for radiation hydrodynamics. The models consist of the compressible Euler equations coupled with moment closure approximations to…
This paper considers systems of balance law with a dissipative non local source. A global in time well posedness result is obtained. Estimates on the dependence of solutions from the flow and from the source term are also provided. The…
This paper establishes limit theorems and quantitative statistical stability for a class of piecewise partially hyperbolic maps that are not necessarily continuous nor locally invertible. By employing a flexible functional-analytic…
Regularization using the L0 pseudo-norm is a common approach to promote sparsity, with widespread applications in machine learning and signal processing. However, solving such problems is known to be NP-hard. Recently, the L0 Bregman…
High-order accurate, $\textit{entropy stable}$ numerical methods for hyperbolic conservation laws have attracted much interest over the last decade, but only a few rigorous convergence results are available, particularly in multiple space…
The linear stability of the homogeneous equilibrium of non-relativistic fluids with mass flux and special relativistic fluids with the absolute value of the energy vector as internal energy is investigated. It is proved that the equilibrium…
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 work is concerned with boundary conditions for one-dimensional hyperbolic relaxation systems with characteristic boundaries. We assume that the relaxation system satisfies the structural stability condition proposed by the second…
In this paper, we continue our investigations of R\'acz's parabolic-hyperbolic formulation of the Einstein vacuum constraints. Our previous studies of the asymptotically flat setting provided strong evidence for unstable asymptotics which…
We study the quantitative small noise limit in the $L^\infty$ norm of certain time-dependent Hamilton-Jacobi equations equipped with Neumann boundary conditions, depending on the regularity of the data and the geometric properties of the…
Linear thresholding models postulate that the conditional distribution of a response variable in terms of covariates differs on the two sides of a (typically unknown) hyperplane in the covariate space. A key goal in such models is to learn…
Exponential stability and solution estimates are investigated for a delay system $$ \dot{x}(t) - A(t)\dot{x}(g(t))=\sum_{k=1}^m B_k(t)x(h_k(t)) $$ of a neutral type, where $A$ and $B_k$ are $n\times n$ bounded matrix functions, and $g, h_k$…
We study the asymptotic behavior of almost-orbits of abstract evolution systems in Banach spaces with or without a Lipschitz assumption. In particular, we establish convergence, convergence in average and almost-convergence of almost-orbits…
Adapting a counterexample recently proposed by J.L. Mancilla-Aguilar and H. Haimovich, we show here that, for time-delay systems, global asymptotic stability does not ensure that solutions converge uniformly to zero over bounded sets of…
We derive an a priori parameter range for overrelaxation of the Sinkhorn algorithm, which guarantees global convergence and a strictly faster asymptotic local convergence. Guided by the spectral analysis of the linearized problem we pursue…
We present a general approach to the problem of determining tight asymptotic lower bounds for generalized central moments of the optimal alignment score of two independent sequences of i.i.d. random variables. At first, these are obtained…
For a class of linear elliptic equations of general type with rapidly oscillating coefficients, we use the sigma-convergence method to prove the homogenization result and a corrector-type result. In the case of asymptotic periodic…
This paper is devoted to the linearized Vlasov-Poisson-Fokker-Planck system in presence of an external potential of confinement. We investigate the large time behaviour of the solutions using hypocoercivity methods and a notion of scalar…
Given a strictly hyperbolic $n\times n$ system of conservation laws, it is well known that there exists a unique Lipschitz semigroup of weak solutions, defined on a domain of functions with small total variation, which are limits of…
For general quadratically-constrained quadratic programming (QCQP), we propose a parabolic relaxation described with convex quadratic constraints. An interesting property of the parabolic relaxation is that the original non-convex feasible…