Instantaneous blowup and singular potentials on Heisenberg groups

TL;DR

This paper extends previous results on instantaneous blowup phenomena to heat equations with singular potentials within the context of Heisenberg groups, highlighting the effects of such potentials on solution behavior.

Contribution

It generalizes earlier blowup results to the setting of the Heisenberg group with singular potentials, expanding understanding of solution singularities in this non-commutative setting.

Findings

Demonstrates conditions leading to instantaneous blowup.

Shows the impact of singular potentials on heat equation solutions.

Extends blowup theory to non-commutative geometric contexts.

Abstract

In this paper we generalize the instantaneous blowup result from [3] and [15] to the heat equation perturbed by singular potentials on the Heisenberg group.