Geodesic
A variational formulation for traveling waves and its applications
Electronic Journal of Differential Equations, Tome 2014 (2014).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this article, we give a variational formulation for traveling wave solutions that decay exponentially at one end of the cylinder for parabolic equations. The variational formulation allows us to obtain the monotone dependence of the velocity on the domain and the nonlinearity, since the velocity is related to the infimum. In particular, we apply this method to Ginzburg-Landau-type problems and a scalar reaction-diffusion-advection equation in infinite cylinders. For the former, we not only obtain the existence, non-existence, boundedness and regularity of the solutions, but also obtain the monotone dependence of the velocity on the nonlinearity and the domain. For the later, we obtain the monotone dependence of the velocity on the nonlinearity and the domain besides the existence, uniqueness, monotonicity and asymptotic behavior at infinity of the solutions. Moreover, we deduce that the influence of the advection on the traveling waves is different from a flow along the cylinder axis considered in many articles.
Classification : 35K57
Keywords: variational formulation, traveling waves, wave velocity 
@article{EJDE_2014__2014__a79,
     author = {Meng, Hai-Xia and Wang, Yu-Xia},
     title = {A variational formulation for traveling waves and its applications},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2014},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a79/}
}
TY  - JOUR
AU  - Meng, Hai-Xia
AU  - Wang, Yu-Xia
TI  - A variational formulation for traveling waves and its applications
JO  - Electronic Journal of Differential Equations
PY  - 2014
VL  - 2014
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a79/
LA  - en
ID  - EJDE_2014__2014__a79
ER  - 
%0 Journal Article
%A Meng, Hai-Xia
%A Wang, Yu-Xia
%T A variational formulation for traveling waves and its applications
%J Electronic Journal of Differential Equations
%D 2014
%V 2014
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a79/
%G en
%F EJDE_2014__2014__a79
Meng, Hai-Xia; Wang, Yu-Xia. A variational formulation for traveling waves and its applications. Electronic Journal of Differential Equations, Tome 2014 (2014). http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a79/