On a parabolic operator of dissipative systems

TL;DR

This paper analyzes a parabolic integro-differential operator relevant to physical phenomena, establishing an equivalence with a third-order equation for Josephson junctions and providing explicit boundary asymptotic analysis.

Contribution

It introduces an equivalence between the parabolic operator and a third-order equation for ESJJ, enabling detailed asymptotic boundary analysis.

Findings

Explicit boundary contributions for the Dirichlet problem are evaluated.

The equivalence facilitates asymptotic analysis of dissipative systems.

The approach links integro-differential operators to physical models in Josephson junctions.

Abstract

A parabolic integro differential operator operator L suitable to describe many phenomena in various physical fields,is considered. By means of equivalence between L and the third order equation which describe the evolution inside an exponentially shaped Josephson junction (ESJJ), an asymptotic analysis for (ESJJ) is achieved, evaluating explicitly boundary contributions related to the Dirichlet problem.