Quasilinear generalized parabolic Anderson model

Ismaël Bailleul (1) , Arnaud Debussche (2) , Martina Hofmanova (3)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 MINGUS - Multi-scale numerical geometric schemes
3 Institut für Mathematik [Berlin]

We provide in this work a local in time well-posedness result for a quasilinear generalized parabolic Anderson model in dimension two∂tu+Δπ(u)=g(u)ξ.The key idea of our approach is a simple transformation of the equation which allows to treat the problem as a semilinear problem. The analysis is done within the setting of paracontrolled calculus.

Mots clés: Singular PDE; Quaslilinear parabolic equation; Paracontrolled calculus

Domaines: Equations aux dérivées partielles [math.AP]

Ismaël Bailleul, Arnaud Debussche, Martina Hofmanova. Quasilinear generalized parabolic Anderson model. Stochastics and Partial Differential Equations: Analysis and Computations, 2019, 7 (1), pp.40-63. ⟨10.1007/s40072-018-0121-1⟩. ⟨hal-01389489⟩