Large-time Behavior for a Cutoff Level-Set Mean Curvature G-equation with Source term
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912855393042432 |
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| author | Calderon, Adrian D. |
| author_facet | Calderon, Adrian D. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_16341 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Large-time Behavior for a Cutoff Level-Set Mean Curvature G-equation with Source term Calderon, Adrian D. Analysis of PDEs 35B40 (Primary), 35B51, 37J51, 49L25 (Secondary) 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. |
| title | Large-time Behavior for a Cutoff Level-Set Mean Curvature G-equation with Source term |
| topic | Analysis of PDEs 35B40 (Primary), 35B51, 37J51, 49L25 (Secondary) |
| url | https://arxiv.org/abs/2509.16341 |