PDE Seminar

Speaker: Tanner Smith (University of Tennessee at Chattanooga)

Title: Optimal mass described by a Sturm-Liouville problem with eigenparameter in the boundary condition: design and predesign

Abstract: We find an optimal mass of a structure described by a Sturm-Liouville (S-L) problem with a spectral parameter in the boundary conditions. While previous work on the subject focused on a somewhat simplified model, we consider a more general S-L problem. We use the calculus of variations approach to determine a set of critical points of the corresponding functional - yet these “predesigns” themselves do not represent meaningful solutions. We additionally introduce a set of solvability conditions on the data of the S-L problem which confirm that these critical points do represent meaningful solutions we refer to as designs.