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We study the quasi-neutral limit in an optimal semiconductor design problem constrained by a nonlinear, nonlocal Poisson equation modelling the drift diffusion equations in thermal equilibrium. While a broad knowledge on the asymptotic…
We prove some new results on existence of solutions to first--order ordinary differential equations with deviating arguments. Delay differential equations are included in our general framework, which even allows deviations to depend on the…
In this article, we addressed the numerical solution of a non-linear evolutionary variational inequality, which is encountered in the investigation of quasi-static contact problems. Our study encompasses both the semi-discrete and…
Quasisymmetry builds a third invariant for charged-particle motion besides energy and magnetic moment. We address quasisymmetry at the level of approximate symmetries of first-order guiding-centre motion. We find that the conditions to…
We considered classical solutions to the initial boundary value problem for non-isentropic compressible Euler equations with damping in multi-dimensions. We obtained global a priori estimates and global existence results of classical…
We introduce a new concept of dissipative measure-valued martingale solutions to the stochastic compressible Euler equations. These solutions are weak in the probabilistic sense i.e., the probability space and the driving Wiener process are…
Both the porous medium equation and the system of isentropic Euler equations can be considered as steepest descents on suitable manifolds of probability measures in the framework of optimal transport theory. By discretizing these…
We study the large time behavior of solutions near a constant equilibrium to the compressible Euler-Maxwell system in $\r3$. We first refine a global existence theorem by assuming that the $H^3$ norm of the initial data is small, but the…
Entropy stabilization of the compressible Euler system is achieved by adapting the averages that are applied to the density and internal energy variables. The approach achieves non-linear robustness despite the use of simplified symmetric…
We develop an energy-decreasing algorithm for the finite element approximation of two-dimensional ferronematic equilibrium states. The problem is formulated as the minimization of the harmonic energy of two two-dimensional vector fields,…
We present a dynamical system framework for understanding Nesterov's accelerated gradient method. In contrast to earlier work, our derivation does not rely on a vanishing step size argument. We show that Nesterov acceleration arises from…
The expectation-maximization (EM) algorithm is a well-known iterative method for computing maximum likelihood estimates from incomplete data. Despite its numerous advantages, a main drawback of the EM algorithm is its frequently observed…
We introduce the concept of maximal dissipative measure-valued solution to the complete Euler system. These are solutions that maximize the entropy production rate. We show that these solutions exist under fairly general hypotheses imposed…
Testing the order of accuracy of (very) high order methods for shallow water (and Euler) equations is a delicate operation and the test cases are the crucial starting point of this operation. We provide a short derivation of vortex-like…
Using min-max inequality we investigate the existence of solutions and thier dependence on parameters for some second order discrete boundary value problem. The approach is based on variational methods and solutions are obtained as saddle…
This paper explores some sufficient conditions for the enhanced solvability of strong vector equilibrium problems, which can be established via a variational approach. Enhanced solvability here means existence of solutions, which are strong…
The convergence and optimality of adaptive mixed finite element methods for the Poisson equation are established in this paper. The main difficulty for mixed finite element methods is the lack of minimization principle and thus the failure…
In this paper we consider the numerical approximation of a general second order semi-linear parabolic partial differential equation. Equations of this type arise in many contexts, such as transport in porous media. Using finite element…
We study the isentropic Euler equations with time-dependent damping, given by $\frac{\mu}{(1+t)^\lambda}\rho u$. Here, $\lambda,\mu$ are two non-negative constants to describe the decay rate of damping with respect to time. We will…
We suggest a new approach for describing quantum dissipation in a small systems for which the system-plus-reservoir approach is not relevant. We first analyze the fact that equilibrium thermodynamics may reveal the existence of an…