Work

On the paradoxical relationship between the heat equation and a traveling-wave solution

Year: 2026

Type: article

Abstract: We investigate the relationship between Brownian motion, which has infinite propagation speed, and a traveling-wave solution with finite propagation speed in the heat equation. First, we define a random walk associated with the Goldstein-Taylor model, a finite-speed approximation of the heat equation. We then introduce a random walk associated with the traveling-wave solutions and analyze its scaling limits, yielding three distinct stochastic processes. Finally, we conclude that the particle motion in a traveling-wave solution includes a mixture of Brownian motion and drift.

Source: Physica A Statistical Mechanics and its Applications

DOI: 10.1016/j.physa.2026.131296

Author: Hironari Miyoshi

Institution: Saitama University

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funder: Waseda University