相关论文: A note on optimal regularity and regularizing effe…
In this paper, we prove optimal convergence rates results for regularisation methods for solving linear ill-posed operator equations in Hilbert spaces. The result generalises existing convergence rates results on optimality to general…
We derive the renormalization group equations for the neutrino masses and mixing angles in explicit form and discuss the possible classes of their solutions. We identify fixed points in the equations for mixing angles, which can be reached…
We study the boundary regularity of solutions to the porous medium equation $u_t = \Delta u^m$ in the degenerate range $m>1$. In particular, we show that in cylinders the Dirichlet problem with positive continuous boundary data on the…
This paper is devoted to prove the exact controllability of a system of N one-dimensional coupled wave equations when the control is exerted on a part of the boundary by means of one control. We consider the case where the coupling matrix A…
This paper is devoted to rigidity results for some elliptic PDEs and related interpolation inequalities of Sobolev type on smooth compact connected Riemannian manifolds without boundaries. Rigidity means that the PDE has no other solution…
The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but…
We consider here asymptotic models that describe the propagation of one-dimensional internal waves at the interface between two layers of immiscible fluids of different densities, under the rigid lid assumption and with uneven bottoms. The…
We present here a survey of recent results concerning the mathematical analysis of instabilities of the interface between two incompressible, non viscous, fluids of constant density and vorticity concentrated on the interface. This…
The performance characteristics of a heat rectifier and a heat pump are studied in a non Markovian framework. The device is constructed from a molecule connected to a hot and cold reservoir. The heat baths are modelled using the stochastic…
We theoretically investigate a quantum heat diode based on two interacting flux qubits coupled to two heat baths. Rectification of heat currents is achieved by asymmetrically coupling the qubits to the reservoirs modelled as dissipative…
We provide a rigorous mathematical analysis of a coupled system consisting of a floating platform in a fluid of finite depth, clamped to a flexible Euler-Bernoulli beam. The superstructure supports a rigid tip mass at its free end,…
Wavelet bases and frames consisting of band limited functions of nearly exponential localization on Rd are a powerful tool in harmonic analysis by making various spaces of functions and distributions more accessible for study and…
We consider the spectral problem for a family of $N$ point interactions of the same strength confined to a manifold with a rotational symmetry, a circle or a sphere, and ask for configurations that optimize the ground state energy of the…
Describing the thermodynamic properties of quantum systems far from equilibrium is challenging, in particular when the system is strongly coupled to its environment, or when memory effects cannot be neglected. Here, we address such regimes…
Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial…
The Majda-Biello system models the interaction of Rossby waves. It consists of two coupled KdV equations one of which has a parameter $\alpha$ as coefficient of its dispersion. This work studies this system on the half line with Robin,…
In this article, we study the the harmonic map heat flow from a manifold with conic singularities to a closed manifold. In particular, we have proved the short time existence and uniqueness of solutions as well as the existence of global…
We establish regularity results for almost-minimizers of a class of variational problems involving both bulk and interface energies. The bulk energy is of Dirichlet type. The surface energy exhibits anisotropic behaviour and is defined by…
This paper investigates the identification of two coefficients in a coupled hyperbolic system with an observation on one component of the solution. Based on the the Carleman estimate for coupled wave equations a logarithmic type stability…
We study coupled quantum systems as the working media of thermodynamic machines. Under a suitable phase-space transformation, the coupled systems can be expressed as a composition of independent subsystems. We find that for the coupled…