caa a22 4500 605515565 CHVBK 20210128100710.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s00205-015-0849-y doi (NATIONALLICENCE)springer-10.1007/s00205-015-0849-y Unique Conservative Solutions to a Variational Wave Equation [Elektronische Daten] [Alberto Bressan, Geng Chen, Qingtian Zhang] Relying on the analysis of characteristics, we prove the uniqueness of conservative solutions to the variational wave equation $${u_{tt} - c (u) (c(u)u_{x}) x = 0}$$ u t t - c ( u ) ( c ( u ) u x ) x = 0 . Given a solution u(t, x), even if the wave speed c(u) is only Hör continuous in the t - x plane, one can still define forward and backward characteristics in a unique way. Using a new set of independent variables X, Y, constant along characteristics, we prove that t, x, u, together with other variables, satisfy a semilinear system with smooth coefficients. From the uniqueness of the solution to this semilinear system, one obtains the uniqueness of conservative solutions to the Cauchy problem for the wave equation with general initial data $${u(0, \cdot) \in H^{1}(I\!R), u_{t} (0, \cdot) \in L^{2}(I\!R).}$$ u ( 0 , · ) ∈ H 1 ( I R ) , u t ( 0 , · ) ∈ L 2 ( I R ) . Springer-Verlag Berlin Heidelberg, 2015 Bressan Alberto Department of Mathematics, Penn State University, 16802, University Park, PA, USA aut Chen Geng School of Mathematics, Georgia Institute of Technology, 30332, Atlanta, GA, USA aut Zhang Qingtian Department of Mathematics, Penn State University, 16802, University Park, PA, USA aut Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 217/3(2015-09-01), 1069-1101 0003-9527 217:3<1069 2015 217 205 https://doi.org/10.1007/s00205-015-0849-y text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00205-015-0849-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bressan Alberto Department of Mathematics, Penn State University, 16802, University Park, PA, USA aut NATIONALLICENCE 700 1- Chen Geng School of Mathematics, Georgia Institute of Technology, 30332, Atlanta, GA, USA aut NATIONALLICENCE 700 1- Zhang Qingtian Department of Mathematics, Penn State University, 16802, University Park, PA, USA aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 217/3(2015-09-01), 1069-1101 0003-9527 217:3<1069 2015 217 205