Local well-posedness of the Cauchy problem for a p-adic Nagumo-type equation

TL;DR

This paper introduces a new class of p-adic nonlinear evolution equations, proves local well-posedness in Sobolev spaces, and demonstrates blow-up phenomena through numerical simulations.

Contribution

It establishes the local well-posedness of a novel family of p-adic Nagumo-type equations and analyzes blow-up behavior for specific subfamilies.

Findings

Proved local well-posedness in Sobolev-type spaces.

Identified blow-up phenomena in certain subfamilies.

Provided numerical simulations illustrating blow-up.

Abstract

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.