A degenerate parabolic-hyperbolic Cauchy problem with a stochastic force

Caroline Bauzet (1) , Guy Vallet (2) , Petra Wittbold (3)

1 I2M - Institut de Mathématiques de Marseille
2 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
3 Essen, Fakultaet fuer Mathematik

In this paper we are interested in the Cauchy problem for a nonlinear degenerate parabolic-hyperbolic problem with multiplicative stochastic forcing. Using an adapted entropy formulation a result of existence and uniqueness of a solution is proved.

Mots clés: Carrillo-Kruzhkov's entropy; Stochastic PDE; degenerate parabolic-hyperbolic equation; Cauchy problem; multiplicative stochastic perturbation; Carrillo-Kruzhkov's entropy.

Domaines: Equations aux dérivées partielles [math.AP]

Caroline Bauzet, Guy Vallet, Petra Wittbold. A degenerate parabolic-hyperbolic Cauchy problem with a stochastic force. Journal of Hyperbolic Differential Equations, 2015, 12 (03), pp.501-533. ⟨10.1142/S0219891615500150⟩. ⟨hal-01003069⟩