Related papers: Application of harmonic analysis techniques to reg…
In this paper we produce new, optimal, regularity results for the solutions to $p$-Poisson equations. We argue through a delicate approximation method, under a smallness regime for the exponent $p$, that imports information from a limiting…
This paper studies the oscillatory behavior of solutions to linear nonautonomous impulsive differential equations with piecewise constant arguments, including both advanced and delayed cases \[ x'(t) = a(t)x(t) + b(t)x([t-k]), \quad k \in…
We study a general convergence theory for the analysis of numerical solutions to the magnetohydrodynamic system describing the time evolution of compressible, viscous, electrically conducting fluids in space dimension d (= 2; 3). First, we…
In many commercial and academic settings, numerical solvers fail to achieve their theoretical performance levels due to issues in the system definition, parameterization, and even implementation. We propose a pair of methods for detecting…
We study partial H\"older regularity for nonlinear elliptic systems in divergence form with double-phase growth, modeling double-phase non-Newtonian fluids in the stationary case.
This paper introduces equivariant hamiltonian flows, a method for learning expressive densities that are invariant with respect to a known Lie-algebra of local symmetry transformations while providing an equivariant representation of the…
As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov…
The purpose of this paper is to establish the regularity the weak solutions for a nonlinear biharmonic equation.
We study constraint satisfaction problems on the so-called 'planted' random ensemble. We show that for a certain class of problems, e.g. graph coloring, many of the properties of the usual random ensemble are quantitatively identical in the…
Compact objects evolving in an astrophysical environment experience a gravitational drag force known as dynamical friction. We present a multipole-frequency decomposition to evaluate the orbit-averaged energy and angular momentum…
Simple aerodynamic configurations under even modest conditions can exhibit complex flows with a wide range of temporal and spatial features. It has become common practice in the analysis of these flows to look for and extract physically…
We present a generalization of dissipative particle dynamics that includes shear forces between particles. The new algorithm has the same structure as the (isothermal) smoothed particle dynamics algorithm, except that it conserves angular…
We discuss some recent advances concerning the symmetry of stochastic differential equations, and in particular the interrelations between these and the integrability -- complete or partial -- of the equations.
Symmetry is a powerful tool for finding analytical solutions to differential equations, both partial and ordinary, via the similarity variables or via the invariance of the equation under group transformations. It is the largest group of…
A large toolbox of numerical schemes for dispersive equations has been established, based on different discretization techniques such as discretizing the variation-of-constants formula (e.g., exponential integrators) or splitting the full…
Following Abbatiello et al. [ DCCDS-A (41), 2020], we introduce dissipative turbulent solutions to a simple model of a mixture of two non interacting compressible fluids {\tc filling a bounded domain with general non zero inflow/outflow…
This article is dedicated to the proof of the existence of classical solutions for a class of non-linear integral variational problems. Those problems are involved in nonlocal image and signal processing.
In this paper it is shown that the compact linearization approach, that has been previously proposed only for binary quadratic problems with assignment constraints, can be generalized to arbitrary linear equations with positive coefficients…
A methodology is proposed for formulating dynamic equations in thermo-piezoelectric and dissipative media from the first principle of energy conservation. The results are in agreement with those from Hamiltonian principle. Our formulations…
Combining analytical and numerical methods, we study within the framework of the homogeneous non-linear Boltzmann equation, a broad class of models relevant for the dynamics of dissipative fluids, including granular gases. We use the new…