Unique Conservative Solutions to a Variational Wave Equation
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| 024 | 7 | 0 | |a 10.1007/s00205-015-0849-y |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00205-015-0849-y | ||
| 245 | 0 | 0 | |a Unique Conservative Solutions to a Variational Wave Equation |h [Elektronische Daten] |c [Alberto Bressan, Geng Chen, Qingtian Zhang] |
| 520 | 3 | |a 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 ) . | |
| 540 | |a Springer-Verlag Berlin Heidelberg, 2015 | ||
| 700 | 1 | |a Bressan |D Alberto |u Department of Mathematics, Penn State University, 16802, University Park, PA, USA |4 aut | |
| 700 | 1 | |a Chen |D Geng |u School of Mathematics, Georgia Institute of Technology, 30332, Atlanta, GA, USA |4 aut | |
| 700 | 1 | |a Zhang |D Qingtian |u Department of Mathematics, Penn State University, 16802, University Park, PA, USA |4 aut | |
| 773 | 0 | |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 217/3(2015-09-01), 1069-1101 |x 0003-9527 |q 217:3<1069 |1 2015 |2 217 |o 205 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00205-015-0849-y |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00205-015-0849-y |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Bressan |D Alberto |u Department of Mathematics, Penn State University, 16802, University Park, PA, USA |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Chen |D Geng |u School of Mathematics, Georgia Institute of Technology, 30332, Atlanta, GA, USA |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Zhang |D Qingtian |u Department of Mathematics, Penn State University, 16802, University Park, PA, USA |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 217/3(2015-09-01), 1069-1101 |x 0003-9527 |q 217:3<1069 |1 2015 |2 217 |o 205 | ||