2015/07/17 by Evan Miller, Miller, Evan, Ari Stern +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Nonlinear Partial Differential Equations #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.1507.05030
openalex publication_date 2015/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The classical heat equation is incompatible with relativity, since the strong maximum principle allows for disturbances to propagate instantaneously. Some authors have proposed limiting the propagation speed by adding a linear hyperbolic correction term, but then even a weak maximum principle fails to hold. We study a more recently introduced relativistic heat equation, which replaces the Laplace operator by a quasilinear elliptic operator, and show that strong and weak maximum principles hold for stationary and time-varying solutions, respectively, as well as for sub- and supersolutions. Moreover, by transforming the equation into an equivalent form, related to the mean curvature operator, we prove even stronger tangency and comparison principles.