Scattering to a stationary solution for the superquintic radial wave equation outside an obstacle

Duyckaerts, Thomas; Yang, Jianwei Urbain

Annales de l'Institut Fourier, Tome 71 (2021) no. 5, pp. 1845-1884.

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.

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.

Classification : 35L71, 35B40, 35L20
Keywords: Wave equation, Stationary wave, Obstacle
Mot clés : Equation des ondes, Solution stationnaire, Obstacle

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