Parameter determination for Energy Balance Models with Memory

TL;DR

This paper investigates Energy Balance Models with Memory in climatology, establishing existence, regularity, uniqueness, and stability results to aid in determining insolation functions within these models.

Contribution

It provides new mathematical results on existence, regularity, and stability for Energy Balance Models with Memory, including methods for determining insolation functions.

Findings

Existence and regularity of solutions established

Uniqueness and stability estimates derived

Methods for parameter determination in models developed

Abstract

In this paper, we study two Energy Balance Models with Memory arising in climatology, which consist in a 1D degenerate nonlinear parabolic equation involving a memory term, and possibly a set-valued reaction term (of Sellers type and of Budyko type, in the usual terminology). We provide existence and regularity results, and obtain uniqueness and stability estimates that are useful for the determination of the insolation function in Sellers' model with memory.