Global Semigroup of Conservative Solutions of the Nonlinear Variational Wave Equation

Abstract

We prove the existence of a global semigroup for conservative solutions of the nonlinear variational wave equation utt − c(u)(c(u)ux)x = 0. We allow for initial data u|t=0 and ut|t=0 that contain measures. We assume that 0 < κ−1 ≤ c(u) ≤ κ. Solutions of this equation may experience concentration of the energy density (ut + c(u) ux)dx into sets of measure… (More)

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