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Qualitative properties of solutions to mixed-diffusion bistable equations

par Bonheure, Denis ;Foldes, Juraj ;Saldana De Fuentes, Alberto
Référence Calculus of variations and partial differential equations, 55, 3, 67
Publication Publié, 2016-06

Article révisé par les pairs

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Résumé :

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 bounded saddle solution in the plane.