*Yaniv Almog*

*ProfessorDepartment of MathematicsLouisiana State University*

Consider a superconducting wire whose temperature is lower than the critical one. When the current through the wire exceeds some critical value, it is well known from experimental observation that the wire becomes resistive, behaving like a normal metal. We prove that the time-dependent Ginzburg-Landau model anticipates this behavior, and obtain upper bound for the critical current. The bounds are obtained in terms of the resolvent of the linearized elliptic operator in ${\mathbb R}^2$ and ${\mathbb R}^2_+$. We then relate this problem to some spectral analysis of a more general class of non-selfadjoint operators.