Globally positive solutions of linear parabolic partial differential equations of second order with Dirichlet boundary conditions

TL;DR

This paper proves that for a linear second order parabolic PDE with Dirichlet boundary conditions on a bounded domain, all globally positive solutions are scalar multiples of each other, establishing a uniqueness property.

Contribution

It establishes the uniqueness (up to positive scalar multiples) of globally positive solutions for a class of linear parabolic PDEs with Dirichlet boundary conditions.

Findings

Globally positive solutions are unique up to multiplication by a positive constant.

The result applies to linear second order parabolic PDEs on bounded domains.

It provides a characterization of positive solutions in this setting.

Abstract

It is shown that globally positive solutions of a linear second order parabolic partial differential equation on a bounded domain, with Dirichlet boundary conditions, are unique up to multiplication by a positive constant.