Related papers: Fukushima's decomposition for diffusions associate…
Nonlinear evolution of a reaction--super-diffusion system near a Hopf bifurcation is studied. Fractional analogues of complex Ginzburg-Landau equation and Kuramoto-Sivashinsky equation are derived, and some of their analytical and numerical…
We consider four different models of nonlinear diffusion equations involving fractional Laplacians and study the existence and properties of classes of self-similar solutions. Such solutions are an important tool in developing the general…
It is well-known that the excursions of a one-dimensional diffusion process can be studied by considering a certain Riccati equation associated with the process. We show that, in many cases of interest, the Riccati equation can be solved in…
In this paper, we revisit the diffusive representations of fractional integrals established in \cite{diethelm2023diffusive} to explore novel variants of such representations which provide highly efficient numerical algorithms for the…
This work studies exact solvability of a class of fractional reaction-diffusion equation with the Riemann-Liouville fractional derivatives on the half-line in terms of the similarity solutions. We derived the conditions for the equation to…
If X is a d-dimensional uniformly elliptic diffusion, with initial law nu, we show that F(X) is a Dirichlet process, whenever F satisfies an integrability condition linking its weak derivative to the coefficients of the diffusion and the…
For diffusion-reaction equations employing a splitting procedure is attractive as it reduces the computational demand and facilitates a parallel implementation. Moreover, it opens up the possibility to construct second-order integrators…
This paper deals with the investigation of a closed form solution of a generalized fractional reaction-diffusion equation. The solution of the proposed problem is developed in a compact form in terms of the H-function by the application of…
Quasiparticle excitations and associated phenomena of energy and momentum transfer rates have been calculated in terms of the drag and the diffusion coefficients exposing clearly the dominance of the magnetic interaction over its electric…
In this letter we address the fragmentation of thin, brittle layers due to the impact of high-velocity projectiles. Our approach is a geometric statistical one, with lines and circles playing the role of cracks, randomly distributed over…
In this paper, we study the large--time behavior of a numerical scheme discretizing drift-- diffusion systems for semiconductors. The numerical method is finite volume in space, implicit in time, and the numerical fluxes are a…
We prove optimal estimates for the decay in time of solutions to a rather general class of non-local in time subdiffusion equations in $\mathbb{R}^d$. An important special case is the time-fractional diffusion equation, which has seen much…
We investigate long-time behaviors of empirical measures associated with subordinated Dirichlet diffusion processes on a compact Riemannian manifold $M$ with boundary $\partial M$ to some reference measure, under the quadratic Wasserstein…
This paper gives a complete characterization of infinitely divisible semimartingales, i.e., semimartingales whose finite dimensional distributions are infinitely divisible. An explicit and essentially unique decomposition of such…
One reports the integral transform that determines the particle size distribution of a given sample from the small-angle scattering intensity under the assumption that the particle correlation function is a polynomial of degree M. The…
In this paper, we study gradient decay estimates for solutions to the multi-dimensional Fisher-KPP equation with fractional diffusion. It is known that this equation exhibits exponentially advancing level sets with strong qualitative upper…
Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…
Sub-diffusion equations are used in a large range of applications including fluids, plasma physics and biology. Their mathematical analysis is advanced even if a much larger literature addresses super-diffusions. The goal of this paper is…
We show that the coalescence model for fragment formation leads to an approximate site percolation model. Features characteristic of a percolation model also appear in microscopic models of disassembly.
Let E be an unbounded open (or closed) domain in Euclidean space of dimension greater or equal to two. We present conservativeness criteria for (possibly reflected) diffusions with state space E that are associated to fairly general…