# ANNALES DE L'INSTITUT FOURIER

Scattering to a stationary solution for the superquintic radial wave equation outside an obstacle
Annales de l'Institut Fourier, Volume 71 (2021) no. 5, pp. 1845-1884.

We consider the focusing wave equation outside a ball of ${ℝ}^{3}$, with Dirichlet boundary condition and a superquintic power nonlinearity. We classify all radial stationary solutions, and prove that all radial global solutions are asymptotically the sum of a stationary solution and a radiation term.

On considère l’équation des ondes focalisante en dehors d’une boule de ${ℝ}^{3}$, avec condition au bord de Dirichlet et une nonlinéarité superquintique. On classifie toutes les solutions radiales stationnaires, et on montre que toutes les solutions radiales globales sont asymptotiquement la somme d’une solution stationnaire et d’un terme de radiation.

Accepted:
Online First:
Published online:
DOI: 10.5802/aif.3447
Classification: 35L71,  35B40,  35L20
Keywords: Wave equation, Stationary wave, Obstacle
Duyckaerts, Thomas 1; Yang, Jianwei Urbain 2

1 Institut Universitaire de France and LAGA (UMR 7359), Institut Galilée, Université Sorbonne Paris Nord 99 avenue Jean-Baptiste Clément 93430 Villetaneuse (France)
2 Department of Mathematics Beijing Institute of Technology Beijing 100081 (P. R. China)
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Duyckaerts, Thomas; Yang, Jianwei Urbain. Scattering to a stationary solution for the superquintic radial wave equation outside an obstacle. Annales de l'Institut Fourier, Volume 71 (2021) no. 5, pp. 1845-1884. doi : 10.5802/aif.3447. https://aif.centre-mersenne.org/articles/10.5802/aif.3447/

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