On spectral problems related to a time dependent model in superconductivity with electric current

Helffer, Bernard

Journées équations aux dérivées partielles (2009), article no. 3, 16 p.

This lecture is mainly inspired by a paper of Y. Almog appearing last year at Siam J. Math. Anal. Our goal here is first to discuss in detail the simplest models which we think are enlightning for understanding the role of the pseudospectra in this question and secondly to present proofs which will have some general character and will for example apply in a more physical model, for which we have obtained recently results together with Y. Almog and X. Pan.

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[AHP] Y. Almog, B. Helffer, and X. Pan. Superconductivity near the normal state under the action of electric currents and induced magnetic field in ${ℝ}^2$. Preprint September 2009, submitted.

[AHHP] Y. Almog, C. Han, B. Helffer, and X. Pan. Critical magnetic field and critical current of type II superconductors. In preparation.

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