相关论文: Quantitative Linear Stability Analysis of Elliptic…

Following Smale, we study simple symmetric mechanical systems of $n$ point particles in the plane. In particular, we address the question of the linear and spectral stability properties of relative equilibria, which are special solutions of…

This thesis studies qualitative properties of solutions to nonlinear elliptic equations of Poisson type with Dirichlet boundary conditions that arise from some physical phenomena, with a particular focus on regularity, stability, and…

For the three-body problem, we consider the Lagrange stability. To analyze the stability, along with integrals of energy and angular momentum, we use relations by the author from Sosnitskii (2005), which band together separately squared…

Here we prove the linear stability of a family of `$n+1$'-dimensional Friedmann Lema\^{i}tre Robertson Walker (FLRW) cosmological models of general relativity. We show that the solutions to the linearized Einstein-Euler field equations…

In the present paper, we build up trace formulas for both the linear Hamiltonian systems and Sturm-Liouville systems. The formula connects the monodromy matrix of a symmetric periodic orbit with the infinite sum of eigenvalues of the…

We consider the inverse problem of determining some class of nonlinear terms appearing in an elliptic equation from boundary measurements. More precisely, we study the stability issue for this class of inverse problems. Under suitable…

This paper deals with an improvement of the "a-priori stability bounds" on the variation of the action variables and on the stability time obtained from a given Birkhoff normal form around the elliptic equilibrium point of an Hamiltonian…

The goal of quantitative elastography is to identify biomechanical parameters from interior displacement data, which are provided by other modalities, such as ultrasound or magnetic resonance imaging. In this paper, we analyze the stability…

The nonlinear stability domain of Lagrange's celebrated 1772 solution of a three-body problem is obtained numerically as a function of the masses of the bodies and the common eccentricity of their Keplerian orbits. This domain shows that…

In this paper we are concerned with the stability of equilibrium solutions of periodic Hamiltonian systems with one degree of freedom in the case of degeneracy, which means that the characteristic exponents of the linearized system have…

PDEs with periodic boundary conditions are frequently used to model processes in large spatial environments, assuming solutions to extend periodically beyond some bounded interval. However, solutions to these PDEs often do not converge to a…

We establish existence, uniqueness and optimal regularity results for very weak solutions to certain nonlinear elliptic boundary value problems. We introduce structural asymptotic assumptions of Uhlenbeck type on the nonlinearity, which are…

In this work, we revisit the planar restricted four-body problem to study the dynamics of an infinitesimal mass under the gravitational force produced by three heavy bodies with unequal masses, forming an equilateral triangle configuration.…

In this paper we study the linear stability of the relative equilibria for homogeneous and quasihomogeneous potentials. Firstly, in the case the potential is a homogeneous function of degree $-a$, we find that any relative equilibrium of…

We establish the existence of weak solutions of a nonlinear radiation-type boundary value problem for elliptic equation on divergence form with discontinuous leading coefficient. Quantitative estimates play a crucial role on the real…

We develop a new geometrical technique to study relative equilibria for a system of $n$--positive masses, moving on the two dimensional sphere $\mathbb{S}^2$, under the influence of a general potential which only depends on the mutual…

We study the secular effects in the motion of an asteroid with negligible mass in a spatial restricted elliptic three body problem with arbitrary inclination. Averaging over mean anomalies of the asteroid and the planet are applied to…

The aim of this paper is to investigate the response of this system/scheme in terms of stability in presence of explicitly treated residual terms, as it inevitably occurs in the reality of NWP. This sudy is restricted to the impact of…

This paper studies the numerical analysis of a parameter identification problem governed by elliptic equations with power-type nonlinearity. We propose a numerical reconstruction via a suitable least-squares minimization problem based on…

In this paper, we consider the elliptic relative equilibria of four-body problem. Here we prove that the corresponding linearized Hamiltonian system at such an elliptic relative equilibria of $4$-bodies splits into two independent linear…