We introduce a new family of p-adic non-linear evolution equations. We establish the local well-posedness of the Cauchy problem for these equations in Sobolev-type spaces. For a certain subfamily, we show that the blow-up phenomenon occurs and provide numerical simulations showing this phenomenon.
Chacón-Cortés, L. F., C. A. Garcia-Bibiano, and W. A. Zúñiga-Galindo. "Local well-posedness of the Cauchy problem for a p-adic Nagumo-type equation." arXiv preprint arXiv:2205.00592 (2022).