| Abstract: |
| This talk explores anisotropic diffusion problems governed by the Finsler Laplacian, with applications in image processing. We establish precise conditions for blow-up at finite time, which can model sharp transitions in tasks like image segmentation. Additionally, we demonstrate global existence for appropriate data, ensuring stability in diffusion-based methods. Finally, we derive explicit exponential decay bounds, providing insights into the long-term behavior of these processes, relevant for efficient image filtering and enhancement. These results offer a rigorous foundation for nonlinear PDE models used not only in computer vision and AI, but also in other areas of science and engineering. |
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