Mathematical Contributions to the Dynamics of the Josephson Junctions: State of the Art and Open Problems

TL;DR

This paper reviews mathematical models of Josephson junctions, analyzing solution behaviors over time and as parameters vary, highlighting open problems and recent rigorous results in the field.

Contribution

It provides a comprehensive overview of current mathematical models, solution analyses, and open problems related to Josephson junctions.

Findings

Analysis of solution behavior as time approaches infinity

Estimates of solutions for small parameters

Identification of open problems in the field

Abstract

Mathematical models related to some Josephson junctions are pointed out and attention is drawn to the solutions of certain initial boundary problems and to some of their estimates. In addition, results of rigorous analysis of the behaviour of these solutions when the time tends to infinity and when the small parameter tends to zero are cited. These analyses lead us to mention some of the open problems.