Geodesic
Weak solutions to a nonlinear variational wave equation and some related problems
Applications of Mathematics, Tome 51 (2006) no. 4, pp. 427-466.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

In this paper we present some results on the global existence of weak solutions to a nonlinear variational wave equation and some related problems. We first introduce the main tools, the $L^p$ Young measure theory and related compactness results, in the first section. Then we use the $L^p$ Young measure theory to prove the global existence of dissipative weak solutions to the asymptotic equation of the nonlinear wave equation, and comment on its relation to Camassa-Holm equations in the second section. In the third section, we prove the global existence of weak solutions to the original nonlinear wave equation under some restrictions on the wave speed. In the last section, we present global existence of renormalized solutions to two-dimensional model equations of the asymptotic equation, which is also the so-called vortex density equation arising from sup-conductivity.
DOI : 10.1007/s10778-006-0111-2
Classification : 35D05, 35L05, 35L50, 35L60
Keywords: variational wave equation; weak solutions; $L^p$ Young measure; renormalized solutions 
@article{10_1007_s10778_006_0111_2,
     author = {Zhang, Ping},
     title = {Weak solutions to a nonlinear variational wave equation and some related problems},
     journal = {Applications of Mathematics},
     pages = {427--466},
     publisher = {mathdoc},
     volume = {51},
     number = {4},
     year = {2006},
     doi = {10.1007/s10778-006-0111-2},
     mrnumber = {2291780},
     zbl = {1164.35330},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10778-006-0111-2/}
}
TY  - JOUR
AU  - Zhang, Ping
TI  - Weak solutions to a nonlinear variational wave equation and some related problems
JO  - Applications of Mathematics
PY  - 2006
SP  - 427
EP  - 466
VL  - 51
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10778-006-0111-2/
DO  - 10.1007/s10778-006-0111-2
LA  - en
ID  - 10_1007_s10778_006_0111_2
ER  - 
%0 Journal Article
%A Zhang, Ping
%T Weak solutions to a nonlinear variational wave equation and some related problems
%J Applications of Mathematics
%D 2006
%P 427-466
%V 51
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10778-006-0111-2/
%R 10.1007/s10778-006-0111-2
%G en
%F 10_1007_s10778_006_0111_2
Zhang, Ping. Weak solutions to a nonlinear variational wave equation and some related problems. Applications of Mathematics, Tome 51 (2006) no. 4, pp. 427-466. doi : 10.1007/s10778-006-0111-2. http://geodesic.mathdoc.fr/articles/10.1007/s10778-006-0111-2/

Cité par Sources :