The paper deals with a third order semilinear equation which characterizes 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 nonlinear, appropriate estimates of this series allow to deduce a priori estimates, continuous dependence and asymptotic behaviour of the solution.
On exponentially shaped Josephson junctions / DE ANGELIS, Monica. - In: ACTA APPLICANDAE MATHEMATICAE. - ISSN 1572-9036. - STAMPA. - 122:1(2012), pp. 179-189. [10.1007/s10440-012-9736-9]
On exponentially shaped Josephson junctions
DE ANGELIS, MONICA
2012
Abstract
The paper deals with a third order semilinear equation which characterizes 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 nonlinear, appropriate estimates of this series allow to deduce a priori estimates, continuous dependence and asymptotic behaviour of the solution.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
