Communications in Mathematical Sciences

Volume 16 (2018)

Number 6

Some mathematical properties of the Weertman equation

Pages: 1729 – 1748



Marc Josien (CERMICS, École des Ponts ParisTech, Marne-la-Valle, France)


We derive here some mathematical properties of the Weertman equation and show that it is the limit of an evolution equation. The Weertman equation is a semilinear integrodifferential equation involving a fractional Laplacian. In addition to this purely theoretical interest, the results proven here give a solid ground to a numerical approach that we have implemented elsewhere.


reaction-advection-diffusion equation, traveling waves, integrodifferential equation, the Weertman equation, fractional Laplacian

2010 Mathematics Subject Classification

26A33, 35K57, 35R11, 45E05

Received 28 February 2018

Accepted 11 May 2018

Published 7 February 2019