Related papers: Nonlinear diffusion of dislocation density and sel…
Straightforward method for the derivation of linearized version of stochastic stability analysis of the nonlinear differential equations is presented. Methods for the study of large time behavior of the moments are exposed. These general…
We study the short-time dynamics of a liquid ligament, held between two solid cylinders, when one is impulsively accelerated along its axis. A set of one-dimensional equations in the slender-slope approximation is used to describe the…
Stationary solutions asymptoting to nonlinear plane waves of the nonlinear Schr\"odinger equation with a PT-symmetric, complex linear potential are characterized. The potential includes both a spatially varying gain-loss profile and a…
In this paper, we introduce and analyze a numerical scheme for solving the Cauchy-Dirichlet problem associated with fractional nonlinear diffusion equations. These equations generalize the porous medium equation and the fast diffusion…
We consider a porous media type equation over all of $\R^d$ with $d = 1$, with monotone discontinuous coefficients with linear growth and prove a probabilistic representation of its solution in terms of an associated microscopic diffusion.…
In this paper we consider a 2D nonlinear and nonlocal model describing the dynamics of the dislocation densities. We prove the local well-posedness of strong solution to this system in the suitable functional framework, and we show the…
In this paper we analyse the asymptotic behaviour of some nonlocal diffusion problems with local reaction term in general metric measure spaces. We find certain classes of nonlinear terms, including logistic type terms, for which solutions…
This paper deals with the existence, monotonicity, uniqueness and asymptotic behaviour of travelling wavefronts for a class of temporally delayed, spatially nonlocal diffusion equations.
The pseudo-spectral method is proposed for following the evolution of density and velocity fluctuations at the weakly non-linear stage in the expanding universe with a good accuracy. In this method, the evolution of density and velocity…
Differential equations need boundary conditions (BC's) for their solution. It is commonly acknowledged that differential equations and BC's are representative of independent physical processes, and no correlations between them is required.…
We give an introduction to discrete functional analysis techniques for stationary and transient diffusion equations. We show how these techniques are used to establish the convergence of various numerical schemes without assuming…
Nonlinear integrable equations serve as a foundation for nonlinear dynamics, and fractional equations are well known in anomalous diffusion. We connect these two fields by presenting the discovery of a new class of integrable fractional…
This is an expository article that describes the spectral-theoretic aspects in the study of the stability of self-similar blowup for nonlinear wave equations. The linearization near a self-similar solution leads to a genuinely…
We apply the postquasistatic approximation, an iterative method for the evolution of self-gravitating spheres of matter, to study the evolution of dissipative and electrically charged distributions in General Relativity. We evolve…
Probably yes, since we find a striking similarity in the spatio-temporal evolution of nonlinear diffusion equations and wave packet spreading in generic nonlinear disordered lattices, including self-similarity and scaling.
In this paper, we investigated a density-dependent reaction-diffusion equation, $u_t = (u^{m})_{xx} + u - u^{m}$. This equation is known as the extension of the Fisher or Kolmogoroff-Petrovsky-Piscounoff equation which is widely used in the…
We examine the short and long-time behaviors of time-fractional diffusion equations with variable space-dependent order. More precisely, we describe the time-evolution of the solution to these equations as the time parameter goes either to…
We find for the first time the asymptotic representation of the solution to the space dependent variable order fractional diffusion and Fokker-Planck equations. We identify a new advection term that causes ultra-slow spatial aggregation of…
The dynamics of thin, non-circular droplets evaporating in the diffusion-limited regime are examined. The challenging non-rectilinear mixed-boundary problem this poses is solved using a novel asymptotic approach and an asymptotic expansion…
A recently proposed nonlinear transport equation is used to model bulk viscous cosmologies that may be far from equilibrium, as happens during viscous fluid inflation or during reheating. The asymptotic stability of the de Sitter and…