Antoniouk, Alexandra2024-05-092024-05-092023-10-24Antoniouk, Oleksandra. (2023). Nonlinear pseudo-differential operators and stochastic equations on p-adic fields. Presentation. Kyiv: American University Kyiv. URI: https://er.auk.edu.ua/handle/234907866/75https://er.auk.edu.ua/handle/234907866/75The p-adic Mathematics is widely used in Theoretical Physics and Biology. It attracts a great deal of interest in quantum mechanics, string theory, quantum gravity, spin-glass theory, and system biology. The concept of a hierarchical energy landscape is very important from the point of view of the description of relaxation phenomena in complex systems, in particular, glasses, clusters, and proteins. This concept can be outlined as follows. A complex system is assumed to have a large number of metastable configurations that realize local minima on the potential energy surface. The local minima are clustered in hierarchically nested basins of minima, namely, each large basin consists of smaller basins, each consisting of even smaller ones, and so on. Thus, the hierarchy of basins possesses ultrametric geometry and transitions between the basins determine the rearrangements of the system configuration for different time scales. Thus the key points of the concept of a hierarchical structure which is typical for p-adic world is the main advantage that can be used for the description of the complex phenomenon. This talk briefly overviews the results related to the theory of pseudo-differential equations in the spaces of test and generalized functions on the field of p-adic numbers. Results related to the modern nonlinear theory of p-adic porous media equations and their solvability.en-USPresentation