Related papers: Limiting absorption principle for the dissipative …
We exhibit a class of singularly perturbed parabolic problems which the asymptotic behavior can be described by a system of ordinary differential equation. We estimate the convergence of attractors in the Hausdorff metric by rate of…
To mitigate pollution effects in high-frequency Helmholtz problems, Learning-based Numerical Methods (LbNM) reconstruct solution operators using complete systems of exact solutions. However, the previously used fundamental-solution (FS)…
For the incompressible and the isentropic compressible Euler equations in arbitrary space dimension, we establish the principle of localised relative energy, thus generalising the well-known relative energy method. To this end, we adapt…
Here we develop a method for investigating global strong solutions of partially dissipative hyperbolic systems in the critical regularity setting. Compared to the recent works by Kawashima and Xu, we use hybrid Besov spaces with different…
In this article we study port-Hamiltonian partial differential equations on certain one-dimensional manifolds. We classify those boundary conditions that give rise to contraction semigroups. As an application we study port-Hamiltonian…
The adsorption phenomenon of neutral particles from the limiting surfaces of the sample in the Langmuir approximation is investigated. The diffusion equation regulating the redistribution of particles in the bulk is assumed to be of…
Compressed Sensing algorithms often make use of the hard thresholding operator to pass from dense vectors to their best s-sparse approximations. However, the output of the hard thresholding operator does not depend on any information from a…
We introduce compactness classes of Hilbert space operators by grouping together all operators for which the associated singular values decay at a certain speed and establish upper bounds for the norm of the resolvent of operators belonging…
In this study, we experimentally investigate the application of a transient signal with complex frequencies to the absorption and transmission of sound waves. Indeed, the emission of a wave with an exponentially varying amplitude in time is…
We characterize the resonances of Stark Hamiltonians by the complex absorbing potential method. Namely, we prove that the Stark resonances are the limit points of complex eigenvalues of the Stark Hamiltonian with a quadratic complex…
The optical theorem is a powerful tool of scattering theory that directly relates the extinction cross section of a scatterer to its forward scattering amplitude. While widely used in electromagnetism and optics, its application in…
We are concerned with the inverse problem of determining both the potential and the damping coefficient in a dissipative wave equation from boundary measurements. We establish stability estimates of logarithmic type when the measurements…
Although the compressible fluid limit of the Boltzmann equation with cutoff has been well investigated in [6] and [13], it still remains largely open to obtain analogous results in case of the angular non-cutoff or even in the grazing limit…
We systematically employ the method of matched asymptotic expansions to model Helmholtz resonators, with thermoviscous effects incorporated starting from first principles and with the lumped parameters characterizing the neck and cavity…
Current simulations of ultraviolet-visible absorption lineshapes, and dynamics of condensed phase systems, largely adopt a harmonic description to model vibrations. Often, this involves a model of displaced harmonic oscillators that have…
We study a finite system of diffusions on the half-line, absorbed when they hit zero, with a correlation effect that is controlled by the proportion of the processes that have been absorbed. As the number of processes in the system becomes…
Our main theorem is in the generality of the axioms of Hilbert space, and the theory of unbounded operators. Consider two Hilbert spaces such that their intersection contains a fixed vector space D. It is of interest to make a precise…
This paper investigates the asymptotic behavior of the Helmholtz free energy of mixtures at small compressibility. We start from a general representation for the local free energy that is valid in stable subregions of the phase diagram. On…
We propose a formulation of an absorbing boundary for a quantum particle. The formulation is based on a Feynman-type integral over trajectories that are confined to the non-absorbing region. Trajectories that reach the absorbing wall are…
The theorem on the existence of maximal nonnegative invariant subspaces for a special class of dissipative operators in Hilbert space with indefinite inner product is proved in the paper. It is shown in addition that the spectra of the…