Seminar talk, 21 February 2018

From Geometry of Differential Equations
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Speaker: Dmitry Tunitsky

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

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.