Study Of Blow-Up Phenomena For P-Adic Semi-Linear Heat Equations

During the last decade a strong and increasing interest in p-adic analysis has arisen, due mainly to its connections with models of complex systems, such as glasses and proteins and, more precisely, with phenomena whose space of states displays a hierarchical structure (see the references) . These phenomena have been modeled using p-adic equations of evolution (p-adic heat equation). The study of solutions to these equations provides relevant information about the evolution of the system under consideration over time. Thus, a quite natural generalization is to consider the semi-linear version of the p-adic heat equation and, therefore, relevant questions concerning the solutions to these equations appear. A particularly interesting question, which is the central topic of this project is to establish appropriate mathematical conditions under which blow-up phenomena for these equations can be established and studied.