Related papers: Subdiffusion with Time-Dependent Coefficients: Imp…
The paper studies the overdamped motion of Brownian particles in a tilted sawtooth potential. The dependencies of the diffusion coefficient and coherence level of Brownian transport on temperature, tilting force, and the shape of the…
We study the qualitative homogenization of second order viscous Hamilton-Jacobi equations in space-time stationary ergodic random environments. Assuming that the Hamiltonian is convex and superquadratic in the momentum variable (gradient)…
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…
Splitting methods constitute a well-established class of numerical schemes for the time integration of partial differential equations. Their main advantages over more traditional schemes are computational efficiency and superior geometric…
We discuss a diffusively perturbed predator-prey system. Freedman and Wolkowicz showed that the corresponding ODE can have a periodic solution that bifurcates from a homoclinic loop. When the diffusion coefficients are large, this solution…
We propose time-domain boundary integral and coupled boundary integral and variational formulations for acoustic scattering by linearly elastic obstacles. Well posedness along with stability and error bounds with explicit time dependence…
We consider the initial/boundary value problem for the fractional diffusion and diffusion-wave equations involving a Caputo fractional derivative in time. We develop two "simple" fully discrete schemes based on the Galerkin finite element…
We derive some regularity estimates of the solution to a time fractional diffusion equation, that are useful for numerical analysis, and partially unravel the singularity structure of the solution with respect to the time variable.
The modelling of linear and nonlinear reaction-subdiffusion processes is more subtle than normal diffusion and causes different phenomena. The resulting equations feature a spatial Laplacian with a temporal memory term through a time…
We provide explicit classical solutions and stochastic analogues for distributed-order space-time fractional diffusion equations on bounded domains with zero exterior boundary conditions. We also show that our results still hold when the…
We begin with a treatment of the Caputo time-fractional diffusion equation, by using the Laplace transform, to obtain a Volterra intego-differential equation where we may examine the weakly singular nature of this convolution…
We develop a complete stability theory for two-dimensional periodic traveling waves of reaction-diffusion systems. More precisely, we identify a diffusive spectral stability assumption, prove that it implies nonlinear stability and provide…
In this paper, we are interested in the propagation of convexity by the strong solution to a one-dimensional Brownian stochastic differential equation with coefficients Lipschitz in the spatial variable uniformly in the time variable and in…
We consider time-harmonic electromagnetic scattering problems on perfectly conducting scatterers with uncertain shape. Thus, the scattered field will also be uncertain. Based on the knowledge of the two-point correlation of the domain…
In this work, an inverse problem in the fractional diffusion equation with random source is considered. Statistical moments are used of the realizations of single point observation $u(x_0,t,\omega).$ We build the representation of the…
This contribution considers the time-fractional subdiffusion with a time-dependent variable-order fractional operator of order $\beta(t)$. It is assumed that $\beta(t)$ is a piecewise constant function with a finite number of jumps. A proof…
We prove duality estimates for time-fractional and more general subdiffusion problems. An important example is given by subdiffusive porous medium type equations. Our estimates can be used to prove uniqueness of weak solutions to such…
A general conversion strategy by involving a shifted parameter $\theta$ is proposed to construct high-order accuracy difference formulas for fractional calculus operators. By converting the second-order backward difference formula with such…
Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the…
Inference-time controllable generation is essential for real-world applications of unconditional diffusion models. However, most existing techniques focus on individual samples, struggling in applications that require the sample population…