In this article we investigate the solution of the steady-state fractional diffusion equation on a bounded domain in ℝ¹. The diffusion operator investigated, motivated by physical considerations, is ...

Aggregation-diffusion equations and gradient flows form a dynamic field of study at the intersection of mathematical analysis, statistical mechanics and applied physics.

HONG WANG, DANPING YANG, SHENGFENG ZHU, INHOMOGENEOUS DIRICHLET BOUNDARY-VALUE PROBLEMS OF SPACE-FRACTIONAL DIFFUSION EQUATIONS AND THEIR FINITE ELEMENT APPROXIMATIONS, SIAM Journal on Numerical ...

The new equation, developed by scientists at the University of Bristol, indicates that diffusive movement through permeable material can be modelled exactly for the very first time. It comes a century ...

These equations are describing the temporal developments of the two distributions u(x,t) und v(x,t). Their dynamics are determined by a local acting reaction term and by a spatial coupling via a ...

This paper develops two local mesh-free methods for designing stencil weights and spatial discretization, respectively, for parabolic partial differential equations (PDEs) of ...