We give a simple proof that the solution of the Allen-Cahn equation converges to Brakke's motion by mean curvature, by utilizing the recent results of Röger and Schätzle in space dimension 2 and 3.

Biofilms form when microorganisms such as certain types of bacteria adhere to the surface of objects in a moist environment and begin to reproduce resulting in the excretion of a slimy glue-like ...

We consider a rough differential equation indexed by a small parameter ε > 0. When the rough differential equation is driven by fractional Brownian motion with Hurst parameter H (1/4 < H < 1/2), we ...

Most people think of history as a series of stories—tales of one army unexpectedly defeating another, or a politician making a memorable speech, or an upstart overthrowing a sitting monarch. Peter ...

A new method developed at the University of Warwick offers the first simple and predictive way to calculate how irregularly ...

Euler’s identity is an equality found in mathematics that has been compared to a Shakespearean sonnet and described as "the most beautiful equation." It is a special case of a foundational equation in ...