Complementary variational principles for a general class of diffusion problems are presented. The theory is illustrated by the electrostatic field and it is shown that Dirichlet's and Thomson's ...

We present an inequality for fractional derivatives related to the Leibniz rule that not only answers positively a conjecture raised by J. I. Diaz, T. Pierantozi, and L. Vázquez but also helps us to ...

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 ...

MIT's Computer Science and Artificial Intelligence Laboratory (CSAIL) has unveiled an innovative AI model that merges principles of diffusion and Poisson Flow. According to MIT News, the researchers ...