相关论文: A rigorous derivation and energetics of a wave equ…

In the present work we consider the electromagnetic wave equation in terms of the fractional derivative of the Caputo type. The order of the derivative being considered is 0 <\gamma<1. A new parameter \sigma, is introduced which…

We use the parabolic and hyperbolic equation with fractional time derivative to describe the subdiffusion in a system with thin membrane. We find the Green's function and solutions of the equation for the system where the homogeneous…

The numerical integration of phase-field equations is a delicate task which needs to recover at the discrete level intrinsic properties of the solution such as energy dissipation and maximum principle. Although the theory of energy…

We develop a wave packet molecular dynamics framework for modeling the structural properties of partially-ionized dense plasmas, based on a chemical model that explicitly includes bound state wavefunctions. Using hydrogen as a…

This survey concerns a causal elastic wave equation which implies frequency power-law attenuation. The wave equation can be derived from a fractional Zener stress-strain relation plus linearized conservation of mass and momentum. A…

This paper is devoted to a numerical analysis of a fractional viscoelastic wave propagation model that generalizes the fractional Maxwell model and the fractional Zener model. First, we convert the model problem into a velocity type…

In this manuscript, we extend the variational multiscale enrichment (VME) method to model the dynamic response of hyperelastic materials undergoing large deformations. This approach enables the simulation of wave propagation under…

Motivated by the analysis of thin structures, we study the variational dimension reduction of hyperelastic energies involving nonlocal gradients to an effective membrane model. When rescaling the thin domain, isotropic interaction ranges…

We present an implicit-explicit (IMEX) scheme for semilinear wave equations with strong damping. By treating the nonlinear, nonstiff term explicitly and the linear, stiff part implicitly, we obtain a method which is not only unconditionally…

We establish the presence of a spectral gap near the real axis for the damped wave equation on a manifold with negative curvature. This results holds under a dynamical condition expressed by the negativity of a topological pressure with…

This work is devoted to infinite-energy solutions of semi-linear wave equations in unbounded smooth domains of $\mathbb{R}^3$ with fractional damping of the form $(-\Delta_x+1)^\frac{1}{2}\partial_t u$. The work extends previously known…

Existing theoretical results for attenuation of surface waves propagating on water of random fluctuating depth are shown to over predict the rate of decay due to the way in which ensemble averaging is performed. A revised approach is…

We investigate the three-dimensional compressible Euler-Maxwell system, a model for simulating the transport of electrons interacting with propagating electromagnetic waves in semiconductor devices. First, we show the global well-posedness…

We study the diffusive scaling limit for a chain of $N$ coupled oscillators. In order to provide the system with good ergodic properties, we perturb the Hamiltonian dynamics with random flips of velocities, so that the energy is locally…

Nonlinear waves in a liquid with gas bubbles are studied. Higher order terms with respect to the small parameter are taken into account in the derivation of the equation for nonlinear waves. A nonlinear differential equation is derived for…

We propose a general connection between entanglement-entropy scaling laws and the linear response functions of particle-conserving fermionic systems in their ground state. Specifically, we show that the response to perturbations coupled to…

We consider a strongly damped semilinear wave equation with initial data prescribed as $(\varrho\phi,\varrho h)$, where the profiles are fixed and only the amplitude $\varrho>0$ is allowed to vary. The question addressed here is how this…

It is shown in linear approximation that in the case of one-dimensional problem of transverse electron waves in a half-infinite slab of homogeneous Maxwellian collisionless plasma with the given boundary field frequency two wave branches of…

The paper studies the interaction of a longitudinal wave with transverse waves in general isotropic and unconstrained hyperelastic materials, including the possibility of dissipation. The dissipative term chosen is similar to the classical…

We prove that the electromagnetic fields in dielectric media whose susceptibility follows a fractional power-law dependence in a wide frequency range can be described by differential equations with time derivatives of noninteger order. We…