Blowup of solutions to a diffusive aggregation model

TL;DR

This paper investigates conditions under which solutions to a diffusive aggregation model blow up in finite time, focusing on the nonexistence of global solutions for equations with Lévy diffusion and general interaction kernels.

Contribution

It provides new criteria for blowup in aggregation equations with Lévy diffusion, extending understanding of solution behavior for a broad class of kernels.

Findings

Identifies conditions leading to finite-time blowup.

Establishes nonexistence of global solutions under certain parameters.

Extends previous results to more general kernels.

Abstract

The nonexistence of global in time solutions is studied for a class of aggregation equations involving L\'evy diffusion operators and general interaction kernels.