Abstract
p-adic wave and diffusion equations are studied on finite T 0-spaces through their Hasse diagrams, which are graphs, and on certain continuous maps called aggregation maps. First, a dictionary between graph theory and p-adic analysis is developed. Then the structure of the solutions of homogeneous wave equations on networks with and without damping is studied and compared with the classical case. Finally, the relationship between the Laplacians of the finite T 0-spaces occurring in aggregation maps is studied. The latter yields a relationship between solutions of such equations on a finite T 0-space and its aggregation to a coarser space.
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Wilson Zúñiga-Galindo is thanked for comments and suggestions which helped to substantially improve this article.
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Bradley, P.E. (2021). p-Adic Wave Equations on Finite Graphs and T 0-Spaces. In: Zúñiga-Galindo, W.A., Toni, B. (eds) Advances in Non-Archimedean Analysis and Applications. STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health. Springer, Cham. https://doi.org/10.1007/978-3-030-81976-7_8
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DOI: https://doi.org/10.1007/978-3-030-81976-7_8
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