相关论文: Birkhoff Normal Form and Hamiltonian PDEs

We elaborate on the interpretation of some mixed finite element spaces in terms of differential forms. First we develop a framework in which we show how tools from algebraic topology can be applied to the study of their cohomological…

We discuss the stability theory and numerical analysis of the Helmholtz equation with variable and possibly non-smooth or oscillatory coefficients. Using the unique continuation principle and the Fredholm alternative, we first give an…

The Bayesian perspective on inverse problems has attracted much mathematical attention in recent years. Particular attention has been paid to Bayesian inverse problems (BIPs) in which the parameter to be inferred lies in an…

In this paper we study a generalized symplectic fixed point problem, first considered by J. Moser in \cite{M}, from the point of view of some relatively recently discovered symplectic rigidity phenomena. This problem has interesting…

We scrutinize the anomalies in diffusion observed in an extended long-range system of classical rotors, the HMF model. Under suitable preparation, the system falls into long-lived quasi-stationary states presenting super-diffusion of rotor…

In multi-phase fluid flow, fluid-structure interaction, and other applications, partial differential equations (PDEs) often arise with discontinuous coefficients and singular sources (e.g., Dirac delta functions). These complexities arise…

Leveraging the techniques found in the literature on Quantum Equilibration for finite dimensional systems, we develop the theory of Quantum Equilibration for the case of infinite-dimensional systems, particularly the cases where the…

We generalize the Linear Combination of Hamiltonian Simulation (LCHS) formula [An, Liu, Lin, Phys. Rev. Lett. 2023] to simulate time-evolution operators in infinite-dimensional spaces, including scenarios involving unbounded operators. This…

This thesis deals with the formulation and analysis of two systems of conservation laws defined on two complementary intervals and coupled by some moving interface as a single infinite-dimensional port-Hamiltonian system. This approach may…

In this paper, we study the Poisson stability (in particular, stationarity, periodicity, quasi-periodicity, Bohr almost periodicity, almost automorphy, recurrence in the sense of Birkhoff, Levitan almost periodicity, pseudo periodicity,…

In this paper, we investigate whether Variational Principles can be associated with the Helmholtz equation subject to impedance (absorbing) boundary conditions. This model has been extensively studied in the literature from both…

In this manuscript, we investigate regularity estimates for a class of quasilinear elliptic equations in the non-divergence form that may exhibit degenerate behavior at critical points of their gradient. The prototype equation under…

We develop a partial Hamiltonian framework to obtain reductions and closed-form solutions via first integrals of current value Hamiltonian systems of ordinary differential equations (ODEs). The approach is algorithmic and applies to many…

The study of self-gravitating stellar systems has provided important hints to develop tools of analytical mechanics. In the present contribution we review how to exploit detuned resonant normal forms to extract information on several…

We present a stability and convergence analysis of the space-time continuous finite element method for the Hamiltonian formulation of the wave equation. More precisely, we prove a continuous dependence of the discrete solution on the data…

We return to the subject of stability of infinite time asymptotics of kinetic equations. We found a model which is simpler than those studied previously and which shows unstable behavior corresponding to our arguments to appear elsewhere,…

The work [8] established memory loss in the time-dependent (non-random) case of uniformly expanding maps of the interval. Here we find conditions under which we have convergence to the normal distribution of the appropriately scaled…

Given a first order dynamical system possessing a commutative algebra of dynamical symmetries, we show that, under certain conditions, there exists a Poisson structure on an open neighbourhood of its regular (not necessarily compact)…

Generalizing ideas of MacKay, and MacKay and Saffman, a necessary condition for the presence of high-frequency ( i.e., not modulational) instabilities of small-amplitude periodic solutions of Hamiltonian partial differential equations is…

We consider the nonlinear cubic Wave, the Hartree and the nonlinear cubic Beam equations on $T^2$ and we prove the existence of different types of solutions which exchange energy between Fourier modes in certain time scales. This exchange…