Seminar talk, 21 February 2018

Speaker: Dmitry Tunitsky

Title: On inverse variational problem for one-dimensional quasilinear wave equation

Abstract:
The talk concerns an inverse problem of calculus of variations for one class of hyperbolic quasilinear second order equations with two independent variables. The equations of this class have a rather wide range of applications, among which are modeling of a two-conductor transmission line, the motion of a hyperelastic homogeneous rod whose cross-sectional area varies along the rod, vibration of a string, wave propagation in a bar of elastic-plastic material, and isentropic flows of a compressible gas with plane symmetry. A constructive solution of the problem in hand is given and the corresponding Lagrangians are explicitly constructed.