相关论文: A Note on the Smoluchowski-Kramers Approximation f…
We obtain variants of the classical Minkowski Theorem on inhomogeneous approximation where we require moreover that the solutions $p, q$ be coprime integers. We link the subject with density exponents of lattice orbits in the real plane.
The Landau equation is a kinetic equation based on the weak coupling approximation of the interaction between the particles. In the framework of dry active matter this new kinetic equation relies on the weak coupling approximation of both…
We compute the effect of quantum mechanical backreaction on the spectrum of radiation in a dynamical moving mirror model, mimicking the effect of a gravitational collapse geometry. Our method is based on the use of a combined WKB and…
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 consider systems of backward stochastic differential equations with c\`adl\`ag upper barrier $U$ and oblique reflection from below driven by an increasing continuous function $H$. Our equations are defined on general probability spaces…
Motivated by the recent results of Andreis-Iyer-Magnanini (2023), we provide a short proof, revisiting the one of Escobedo-Mischler-Perthame (2002), that for a large class of coagulation kernels, any weak solution to the Smoluchowski…
By using determinantal representations of the W-weighted Drazin inverse previously obtained by the author within the framework of the theory of the column-row determinants, we get explicit formulas for determinantal representations of the…
In this paper, we look at quasiconformal solutions $\phi:\mathbb{C}\to\mathbb{C}$ of Beltrami equations $$ \partial_{\overline{z}} \phi(z)=\mu(z)\,\partial_z \phi (z). $$ where $\mu\in L^\infty(\mathbb{C})$ is compactly supported on…
In this paper we first study the penalization approximation of stochastic differential equations reflected in a domain which satisfies conditions (A) and (B) and prove that the sequence of solutions of the penalizing equations converges in…
In this paper we study a second-order mean-field stochastic differential systems describing the movement of a particle under the influence of a time-dependent force, a friction, a mean-field interaction and a space and time-dependent…
Main objects of the paper are stationary and weak KAM Hamilton-Jacobi equations on the finite-dimensional torus. The key idea of the paper is to replace the underlying calculus of variations problems with continuous time Markov decision…
In the numerical treatment of large-scale Sylvester and Lyapunov equations, projection methods require solving a reduced problem to check convergence. As the approximation space expands, this solution takes an increasing portion of the…
Finding the eigenvalues of a Sturm-Liouville problem can be a computationally challenging task, especially when a large set of eigenvalues is computed, or just when particularly large eigenvalues are sought. This is a consequence of the…
We use the Landweber method for numerical simulations for the multiwave tomography problem with a reflecting boundary and compare it with the averaged time reversal method. We also analyze the rate of convergence and the dependence on the…
In the following paper, one studies, given a bounded, connected open set $\Omega$ $\subseteq$ R n , $\kappa$ > 0, a positive Radon measure $\mu$ 0 in $\Omega$ and a (signed) Radon measure $\mu$ on $\Omega$ satisfying $\mu$($\Omega$) = 0 and…
The aim of this article is to introduce a bivariate extension of Shurer-Stancu operators based on (p q)integers. We prove uniform approximation by means of Bohman Korovkin type theorem rate of convergence using total modulus of smoothness…
The Smoluchowsky equation for a system of interacting Brownian particles in a temperature gradient is derived from the Kramers equation by means of a multiple time-scale method. The interparticle interactions are assumed to be represented…
We present a numerical framework to approximate the $\mu$-domain in the planar Skorokhod embedding problem (PSEP), recently appeared in \cite{gross2019}. Our approach investigates the continuity and convergence properties of the solutions…
The question of triviality of solutions of the semilinear Ornstein-Uhlenbeck equation, \[ \Delta w-\frac{1}{2} \langle x,\nabla w\rangle-\frac{\lambda}{p-1}w+|w|^{p-1}w=0, \] is considered. It is shown, that if $p>1$ is Sobolev subcritical…
We investigate the inverse problem of recovering the diffusion and absorption coefficients $(\sigma,q)$ in the nonlocal diffuse optical tomography equation $(-\text{div}( \sigma \nabla))^s u+q u =0 \text{ in }\Omega$ from the nonlocal…