Large-time Behavior for a Cutoff Level-Set Mean Curvature G-equation with Source term

2025/09/19 by Adrian D. Calderon, Calderon, Adrian D.
Mathematics · Engineering · #Advanced Mathematical Physics Problems #Nonlinear Partial Differential Equations #Computational Fluid Dynamics and Aerodynamics

paper · pdf · doi:10.48550/arxiv.2509.16341

Abstract

We consider a cutoff level-set mean curvature G-equation with a non-negative source term. In particular, we study the large-time behavior of this fully nonlinear degenerate parabolic partial differential equation in two settings: periodic and radially symmetric. Due to the non-coercivity and non-convexity of the Hamiltonian, we are not able to use the standard Hamilton-Jacobi theory and instead rely on the inherent structure to find a monotonicity property and corresponding uniqueness set. Lastly, we discuss the local regularity of the solutions, as well as a representation formula in the radial symmetric setting.

Citations

• Does Yakhot's growth law for turbulent burning velocity hold?
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