Related papers: Energy decay for evolution equations with glassy t…
Electron dynamics in metallic clusters are examined using a time-dependent density functional theory that includes a 'memory term', i.e. attempts to describe temporal non-local correlations. Using the Iwamoto, Gross and Kohn…
We consider the question of exponential decay to equilibrium of solutions of an abstract class of degenerate evolution equations on a Hilbert space modeling the steady Boltzmann and other kinetic equations. Specifically, we provide…
The paper is devoted to understand the large time behaviour and decay of the solution of the discrete heat equation in the one dimensional mesh $\Z$ on $\ell^p$ spaces, and its analogies with the continuous-space case. We do a deep study of…
Evolution equations of YFS and DGLAP types in leading order are considered. They are compared in terms of mathematical properties and solutions. In particular, it is discussed how the properties of evolution kernels affect solutions.…
We consider damped wave equations with a potential and rotational inertia terms. We study the Cauchy problem for this model in the one dimensional Euclidean space and we obtain fast energy decay and L^2-decay of the solution itself as time…
It is known that the asymptotic behavior of time-dependent dissipative coefficient in the Cauchy problem of dissipative wave equation dominates the energy decay estimate. In particular, it is important to study the case where the…
Several papers have recently presented results of measurements of physical aging by studying the behavior of glassy materials quenched from temperatures above their glass transition temperature $T_g$. The evolution of the aging process is…
We reconsider the evolution of strongly degenerate neutrinos in the early universe. Our chief concern is the validity of the entropy conservation after the neutrino annihilation process has frozen out (so that the establishment of chemical…
Energy decay is established for the damped wave equation on compact Riemannian manifolds where the damping coefficient is allowed to depend on time. Using a time dependent observability inequality, it is shown that the energy of solutions…
With the ever-growing adoption of AI, its impact on the environment is no longer negligible. Despite the potential that continual learning could have towards Green AI, its environmental sustainability remains relatively uncharted. In this…
This work analyzes the finite element approximation to a viscoelastic flow model, which generalizes the Navier-Stokes equation and Oldroyd's model by introducing the tempered power-law memory kernel. We prove regularity and long-time…
We develop the theory of fractional gradient flows: an evolution aimed at the minimization of a convex, l.s.c.~energy, with memory effects. This memory is characterized by the fact that the negative of the (sub)gradient of the energy equals…
Elastic models of the glass transition relate the relaxation dynamics and the elastic properties of structural glasses. They are based on the assumption that the relaxation dynamics occurs through activated events in the energy landscape…
We identify a link between the glass transition and percolation of mobile regions in configuration space. We find that many hallmarks of glassy dynamics, for example stretched-exponential response functions and a diverging structural…
Decaying vacuum models are a class of models that incorporate the vacuum energy density as a time-evolving entity that has the potential to explain the entire evolutionary history of the universe in a single framework. A general solution to…
In this note, we analyze an abstract evolution equation with time-dependent time delay and time-dependent delay feedback coefficient. We assume that the operator corresponding to the nondelayed part of the model generates an exponentially…
We consider the evolution of the temperature $u$ in a material with thermal memory characterized by a time-dependent convolution kernel $h$. The material occupies a bounded region $\Omega$ with a feedback device controlling the external…
Recent observations demonstrate that densely packed tissues exhibit features of glassy dynamics, such as caging behavior and dynamical heterogeneities, although it has remained unclear how single-cell properties control this behavior. Here…
A degenerate Schr\"{o}dinger equation under fractional integral damping is considered. Here the damping term is singular and not integrable and we consider the two cases when damping acting on the degenerate boundary and nondegenerate…
This work rigorously implements a recent model of large-strain elasto-plastic evolution in single crystals where the plastic flow is driven by the movement of discrete dislocation lines. The model is geometrically and elastically nonlinear,…