Related papers: Fractional wave equation and damped waves
In this work, we are concerned with a nonlinear wave equation with variable exponents. A distributive delay is imposed into the damping term with variable exponents nonlinearity. Firstly, we show that the global nonexistence time can be…
We introduce a fractional Kramers equation for a particle interacting with a thermal heat bath and external non-linear force field. For the force free case the velocity damping follows the Mittag-Leffler relaxation and the diffusion is…
This article analysis differential equations which represents damped and fractional oscillators. First, it is shown that prior to using physical quantities in fractional calculus, it is imperative that they are turned dimensionless.…
This paper is devoted to study the wave propagation and its stability for a class of two-component discrete diffusive systems. We first establish the existence of positive monotone monostable traveling wave fronts. Then, applying the…
Using the method of a priori energy estimates, energy dissipation is proved for the class of hereditary fractional wave equations, obtained through the system of equations consisting of equation of motion, strain, and fractional order…
This work considers the variable-exponent fractional diffusion-wave equation, which describes, e.g. the propagation of mechanical diffusive waves in viscoelastic media with varying material properties. Rigorous numerical analysis for this…
A fundamental non-classical fourth-order partial differential equation to describe small amplitude linear oscillations in a rotating compressible fluid, is obtained. The dispersion relations for such a fluid, and the different regions of…
In this paper we consider the Benjamin equation, a partial differential equation that models one-way propagation of long internal waves of small amplitude along the interface of two fluid layers under the effects of gravity and surface…
We study a 2D lattice model of forward-directed waves in which the integrated intensity for classical waves (or probability for quantum mechanical particles) is conserved. The model describes the time evolution of 1D quantum particle in a…
We consider two dimensional nonstationary scattering of plane waves by a NN-wedge. We prove the existence and uniqueness of a solution to the corresponding mixed problem and we give an explicit formula for the solution. Also the Limiting…
A condition which guaranties the exponential decay of the solutions of the initial-boundary value problem for the damped wave equation is proved. A method for the effective computability of the coefficient of exponential decay is also…
We investigate anomalous diffusion processes governed by the fractional Langevin equation and confined to a finite or semi-infinite interval by reflecting potential barriers. As the random and damping forces in the fractional Langevin…
We investigate a local modification of a variable-order fractional wave equation, which describes the propagation of diffusive wave in viscoelastic media with evolving physical property. We incorporate an equivalent formulation to prove the…
Starting from kicked equations of motion with derivatives of non-integer orders, we obtain "fractional" discrete maps. These maps are generalizations of well-known universal, standard, dissipative, kicked damped rotator maps. The main…
In this paper we investigate the following fractional order in time Cauchy problem \begin{equation*} \begin{cases} \mathbb{D}_{t}^{\alpha }u(t)+Au(t)=f(u(t)), & 1<\alpha <2, u(0)=u_{0},\,\,\,u^{\prime }(0)=u_{1}. & \end{cases}%…
The diffusion equation and its time-fractional counterpart can be obtained via the diffusion limit of continuous-time random walks with exponential and heavy-tailed waiting time distributions. The space dependent variable-order…
This paper is concerned with the propagation dynamics of time almost periodic reaction-diffusion equations. Assuming the existence of a time almost periodic traveling wave connecting two stable steady states, we focus especially on the…
We consider the fundamental solution to the wave equation on a manifold with corners of arbitrary codimension. If the initial pole of the solution is appropriately situated, we show that the singularities which are diffracted by the corners…
We establish space-time dispersive estimates for solutions to the wave equation on compact Riemannian manifolds with bounded sectional curvature, with the same exponents as for $C^\infty$ metrics. The estimates are for bounded time…
We advance an exact, explicit form for the solutions to the fractional diffusion-advection equation. Numerical analysis of this equation shows that its solutions resemble power-laws.