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arXiv · 2509.16341

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

Adrian D. Calderon
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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.

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Adrian D. Calderon. 2025-09-19. Large-time Behavior for a Cutoff Level-Set Mean Curvature G-equation with Source term. https://arxiv.org/abs/2509.16341

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