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

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.

11 pages

References in corpus (2)

• Existence and uniqueness of solutions of a class of 3rd order dissipative problems with various boundary conditions describing the Josephson effect
• Existence and uniqueness results for a class of non linear models

Cited by in corpus (3)

• On the transition from parabolicity to hyperbolicity for a nonlinear equation under Neumann boundary conditions
• A wave equation perturbed by viscous terms: fast and slow times diffusion effects in a Neumann problem
• On diffusion effects of the perturbed sine-Gordon equation with Neumann boundary conditions