Travelling graphs for the forced mean curvature motion in an arbitrary space dimension
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 46 (2013) no. 2, p. 217-248

We construct travelling wave graphs of the form z=-ct+φ(x), φ:x N-1 φ(x), N2, solutions to the N-dimensional forced mean curvature motion V n =-c 0 +κ (cc 0 ) with prescribed asymptotics. For any 1-homogeneous function φ , viscosity solution to the eikonal equation |Dφ |=(c/c 0 ) 2 -1, we exhibit a smooth concave solution to the forced mean curvature motion whose asymptotics is driven by φ . We also describe φ in terms of a probability measure on  𝕊 N - 2 .

Nous construisons des ondes progressives sous la forme de graphes z=-ct+φ(x), φ:x N-1 φ(x), N2, solutions du mouvement par courbure moyenne forcée V n =-c 0 +κ (cc 0 ) en dimension N d’espace et avec un comportement asymptotique prescrit. Pour toute solution de viscosité φ , 1-homogène en espace, de l’équation eikonale |Dφ |=(c/c 0 ) 2 -1, nous mettons en évidence une solution régulière et concave du mouvement par courbure moyenne forcée dont le comportement asymptotique est donné par φ . Nous décrivons aussi φ en terme d’une mesure de probabilité sur la sphère 𝕊 N - 2 .

DOI : https://doi.org/10.24033/asens.2188
Classification:  53C44,  35F21,  35C07,  35D40,  35K57
Keywords: forced mean curvature movement, eikonal equation, Hamilton-Jacobi equations, viscosity solution, reaction diffusion equations, travelling fronts
@article{ASENS_2013_4_46_2_217_0,
     author = {Monneau, R\'egis and Roquejoffre, Jean-Michel and Roussier-Michon, Violaine},
     title = {Travelling graphs for the forced mean curvature motion in an arbitrary space dimension},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {Ser. 4, 46},
     number = {2},
     year = {2013},
     pages = {217-248},
     doi = {10.24033/asens.2188},
     language = {en},
     url = {http://www.numdam.org/item/ASENS_2013_4_46_2_217_0}
}
Monneau, Régis; Roquejoffre, Jean-Michel; Roussier-Michon, Violaine. Travelling graphs for the forced mean curvature motion in an arbitrary space dimension. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 46 (2013) no. 2, pp. 217-248. doi : 10.24033/asens.2188. http://www.numdam.org/item/ASENS_2013_4_46_2_217_0/

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