Qualitative properties of solutions to mixed-diffusion bistable equations

Denis Bonheure (1, 2) , Földes Juraj (2) , Saldaña Alberto (2)

1 MEPHYSTO - Quantitative methods for stochastic models in physics
2 Département de mathématiques Université Libre de Bruxelles

We consider a fourth-order extension of the Allen-Cahn model with mixed-diffusion and Navier boundary conditions. Using variational and bifurcation methods, we prove results on existence, uniqueness, positivity, stability, a priori estimates, and symmetry of solutions. As an application, we construct a nontrivial bounded saddle solution in the plane.

Domaines: Equations aux dérivées partielles [math.AP]

Denis Bonheure, Földes Juraj, Saldaña Alberto. Qualitative properties of solutions to mixed-diffusion bistable equations. Calculus of Variations and Partial Differential Equations, 2016, 55, ⟨10.1007/s00526-016-0987-6⟩. ⟨hal-01203710⟩