Related papers: From anomalous to classical diffusion in a non-lin…
We explain the ubiquity and extremely slow evolution of non gaussian out-of-equilibrium distributions for the Hamiltonian Mean-Field model, by means of traditional kinetic theory. Deriving the Fokker-Planck equation for a test particle, one…
When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model, for example, the orders of the fractional derivative or the source term, are often unknown,…
We analyze a quasi-continuous linear chain with self-similar distribution of harmonic interparticle springs as recently introduced for one dimension (Michelitsch et al., Phys. Rev. E 80, 011135 (2009)). We define a continuum limit for one…
We consider an equation with drift and either critical or supercritical fractional diffusion. Under a regularity assumption for the vector field that is marginally stronger than what is required for Holder continuity of the solutions, we…
In this paper, a new fractional operator of variable order with the use of the monotonic increasing function is proposed in sense of Caputo type. The properties in term of the Laplace and Fourier transforms are analyzed and the results for…
This review article aims to stress and reunite some of the analytic formalism of the anomalous diffusive processes that have succeeded in their description. Also, it has the objective to discuss which of the new directions they have taken…
Lie group method provides an efficient tool to solve a differential equation. This paper suggests a fractional partner for fractional partial differential equations using a fractional characteristic method. A space-time fractional diffusion…
Simple finite differencing of the anisotropic diffusion equation, where diffusion is only along a given direction, does not ensure that the numerically calculated heat fluxes are in the correct direction. This can lead to negative…
We show how to use a central limit approximation for additive co-cycles to describe non-equilibrium and far from equilibrium thermodynamic behavior. We consider first two weakly coupled Hamiltonian dynamical systems initially at different…
We study the regularity properties of the solutions to the nonlinear equation with fractional diffusion $$ \partial_tu+(-\Delta)^{\sigma/2}\varphi(u)=0, $$ posed for $x\in \mathbb{R}^N$, $t>0$, with $0<\sigma<2$, $N\ge1$. If the…
In this paper, we consider a linear heat equation with constant coefficients and a single constant delay. Such equations are commonly used to model and study various problems arising in ecology and population biology when describing the…
By considering the master equation of the partially asymmetric diffusion process on a one-dimensional lattice, the most general boundary condition (i.e. interactions) for the multi-species reaction-diffusion processes is considered.…
We first study the so-called Heat equation with two families of elliptic operators whichare fully nonlinear, and depend on some eigenvalues of the Hessian matrix. The equationwith operators including the "large" eigenvalues has strong…
We consider a diffusion process on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ an energetic variational approach with both surface divergence and transport theorems to derive…
Fractional equations have become the model of choice in several applications where heterogeneities at the microstructure result in anomalous diffusive behavior at the macroscale. In this work we introduce a new fractional operator…
We examine the validity of the principle of mass conservation for solutions of some typical equations in the theory of nonlinear diffusion, including equations in standard differential form and also their fractional counterparts. In Part 1,…
We generalize the method of obtaining the fundamental linear partial differential equations such as the diffusion and Schrodinger equation, Dirac and telegrapher's equation from a simple stochastic consideration to arrive at certain…
We continue the study of a model for heat conduction consisting of a chain of non-linear oscillators coupled to two Hamiltonian heat reservoirs at different temperatures. We establish existence of a Liapunov function for the chain dynamics…
We study the link between relaxation to the equilibrium and anomalous superdiffusive motion in a classical N-body hamiltonian system with long-range interaction showing a second-order phase-transition in the canonical ensemble. Anomalous…
In this work we study the degenerate diffusion equation $\partial_{t}=x^{\alpha}a\left(x\right)\partial_{x}^{2}+b\left(x\right)\partial_{x}$ for $\left(x,t\right)\in\left(0,\infty\right)^{2}$, equipped with a Cauchy initial data and the…