Front localization in a ballistic annihilation model

TL;DR

This paper investigates conditions under which a front remains localized in a one-dimensional ballistic annihilation model with initially separated species, demonstrating that certain initial conditions lead to persistent localization.

Contribution

The study introduces two classes of initial conditions that guarantee the localization of the front in a ballistic annihilation model.

Findings

Front remains localized under specific initial conditions

Constructed explicit classes of initial conditions for localization

Provides theoretical framework for front localization in ballistic models

Abstract

We study the possibility of localization of the front present in a one-dimensional ballistically-controlled annihilation model in which the two annihilating species are initially spatially separated. We construct two different classes of initial conditions, for which the front remains localized.