相关论文: The fragmentation equation with size diffusion: Sm…
Stationary probability distributions of one-dimensional random walks on lattices with aperiodic disorder are investigated. The pattern of the distribution is closely related to the diffusional behavior, which depends on the wandering…
The fragmentation of small, brittle, flexible, inextensible fibers is investigated in a fully-developed, homogeneous, isotropic turbulent flow. Such small fibers spend most of their time fully stretched and their dynamics follows that of…
A non--linear diffusion equation is derived by taking into account hopping rates depending on the occupation of next neighbouring sites. There appears additonal repulsive and attractive forces leading to a changed local mobiltiy. The…
In this paper we study a convection-reaction-diffusion equation of the form \begin{equation*} u_t=\varepsilon(h(u)u_x)_x-f(u)_x+f'(u), \quad t>0, \end{equation*} with a nonlinear diffusion in a bounded interval of the real line. In…
We present results from an individual particle based model for the collision, coagulation and fragmentation of heavy drops moving in a turbulent flow. Such a model framework can help to bridge the gap between the full hydrodynamic…
We study the large time behaviour of the mass (size) of particles described by the fragmentation equation with homogeneous breakup kernel. We give necessary and sufficient conditions for the convergence of solutions to the unique…
We investigate stationary solutions of a non-local aggregation equation with degenerate power-law diffusion and bounded attractive potential in arbitrary dimensions. Compact stationary solutions are characterized and compactness…
In this paper, classical small perturbations against a stationary solution of the nonlinear Schrodinger equation with the general form of nonlinearity are examined. It is shown that in order to obtain correct (in particular, conserved over…
A mathematical model for the discrete nonlinear fragmentation (collision-induced breakage) equation with diffusion is studied. The existence of global weak solutions is established in arbitrary spatial dimensions without assuming a strictly…
We study the behaviour of the solutions of the stationary diffusion equation as a function of a possibly rough ($L^{\infty}$-) diffusivity. This includes the boundary behaviour of the solution maps, associating to each diffusivity the…
The behaviour of the solutions of the time-fractional diffusion equation, based on the Caputo derivative, is studied and its dependence on the fractional exponent is analysed. The time-fractional convection-diffusion equation is also solved…
Reaction-diffusion equations coupled to ordinary differential equations (ODEs) may exhibit spatially low-regular stationary solutions. This work provides a comprehensive theory of asymptotic stability of bounded, discontinuous or…
We investigate systems of nature where the common physical processes diffusion and fragmentation compete. We derive a rate equation for the size distribution of fragments. The equation leads to a third order differential equation which we…
We introduce three models of fragmentation in which the largest fragment in the system can be broken at each time step with a fixed probability, p. We solve these models exactly in the long time limit to reveal stable time invariant…
In the present work, the behavior of vacancy pore inside of spherical particle is investigated. On the assumption of quasistationarity of diffusion fluxes, the nonlinear equation set was obtained analytically, that describes completely pore…
We consider a model of fragmentation of sheet by cracks that move with a velocity in preferred direction, but undergo random transverse displacements as they move. There is a non-zero probability of crack-splitting, and the split cracks…
This paper investigates the well-posedness and small-noise asymptotics of a class of stochastic partial differential equations defined on a bounded domain of $\mathbb{R}^d$, where the diffusion coefficient depends nonlinearly and…
An explicit solution for a growth fragmentation equation with constant dislocation measure is obtained. In this example the necessary condition for the general results in \cite{BW} about the existence of global solutions in the so called…
We present a simple numerical model for investigating the general properties of fragmentation. By use of molecular dynamics simulations, we study the impact fragmentation of a solid disk of interacting particles with a wall. Regardless of…
The scaling invariance for chaotic orbits near a transition from unlimited to limited diffusion in a dissipative standard mapping is explained via the analytical solution of the diffusion equation. It gives the probability of observing a…