On pseudo-spectral problems related to a time-dependent model in superconductivity with electric current
The paper under review is motivated by the study of the effect of the electric current in a problem arising in superconductivity theory. In the first part of the present paper there are given proofs with some general character and which are applied to a more physical model that involves the non-self-adjoint differential operator \(-\partial^2_x-(\partial_y-ix^2/2)^2+icy\) (\(c\not=0\)) on \({\mathbb R}^2_{x,y}\). The next section is devoted to a pseudo-spectral analysis of the complex Airy operator \(D_x^2+ix\) (with \(D_x=-i\frac{d}{dx}\)) both on the real axis and on \({\mathbb R}^+\).
scientific article