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
Inria Lille - Nord Europe, ULB - Université Libre de Bruxelles [Bruxelles], LPP - Laboratoire Paul Painlevé - UMR 8524
Abstract : 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.
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Denis Bonheure, Földes Juraj, Saldaña Alberto. Qualitative properties of solutions to mixed-diffusion bistable equations. Calculus of Variations and Partial Differential Equations, Springer Verlag, 2016, 55, ⟨10.1007/s00526-016-0987-6⟩. ⟨hal-01203710⟩

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