On exponentially shaped Josephson junctions
Monica De Angelis
TL;DR
This paper analyzes a third order semilinear equation modeling exponentially shaped Josephson junctions, providing explicit solutions for linear sources and qualitative analysis for nonlinear cases.
Contribution
It offers explicit Fourier series solutions for linear cases and establishes a priori estimates and asymptotic behavior for nonlinear cases.
Findings
Explicit solutions for linear source terms
A priori estimates for nonlinear solutions
Analysis of asymptotic behavior
Abstract
The paper deals with a third order semilinear equation which char- acterizes exponentially shaped Josephson junctions in superconductivity. The initial-boundary problem with Dirichlet conditions is analyzed. When the source term F is a linear function, the problem is explicitly solved by means of a Fourier series with properties of rapid convergence. When F is nonlin- ear, appropriate estimates of this series allow to deduce a priori estimates, continuous dependence and asymptotic behaviour of the solution.
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Taxonomy
TopicsPhysics of Superconductivity and Magnetism · Spectral Theory in Mathematical Physics · Stability and Controllability of Differential Equations