Mathematical properties of the Weertman equation
Marc Josien
TL;DR
This paper investigates the mathematical properties of the Weertman equation, a fractional Laplacian integrodifferential equation, establishing its theoretical foundation and connection to an evolution equation, supporting numerical methods.
Contribution
It provides new mathematical insights into the Weertman equation and links it to an evolution equation, enhancing understanding and numerical analysis.
Findings
Proves mathematical properties of the Weertman equation.
Shows the equation as the limit of an evolution process.
Supports numerical approaches with theoretical validation.
Abstract
We derive here some mathematical properties of the Weertman equation and show 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 (see arXiv:1704.04489).
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Taxonomy
TopicsNonlinear Differential Equations Analysis · Nonlinear Partial Differential Equations · Fractional Differential Equations Solutions