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

Green's functions and propagators for the multi-dimensional anisotropic space-time fractional diffusion equation are obtained in integral form. Uniqueness of the solutions is studied in the framework ...

SIAM Journal on Applied Mathematics, Vol. 39, No. 2 (Oct., 1980), pp. 272-289 (18 pages) In this paper we consider the determination of an unknown diffusion coefficient in a nonlinear diffusion ...

Observing nature shows that many temporal and spatial structures are not formed by the outside, but rather by the respective system itself. To study these self-organizing processes is the subject of ...

A groundbreaking mathematical equation has been discovered, which could transform medical procedures, natural gas extraction, and plastic packaging production in the future. The new equation, ...