Some mathematical properties of the Weertman equation

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.

Keywords

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

2010 Mathematics Subject Classification

26A33, 35K57, 35R11, 45E05

Full Text (PDF format)

Received 28 February 2018

Accepted 11 May 2018

Published 7 February 2019