Mathematical analysis of a nonlinear parabolic equation arising in the modelling of non-newtonian flows

Eric Cancès (1) , Isabelle Catto (2) , Yousra Gati (1)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

The mathematical properties of a nonlinear parabolic equation arising in the modelling of non-newtonian flows are investigated. The peculiarity of this equation is that it may degenerate into a hyperbolic equation (in fact a linear advection equation). Depending on the initial data, at least two situations can be encountered: the equation may have a unique solution in a convenient class, or it may have infinitely many solutions.

Domaines: Equations aux dérivées partielles [math.AP]

Eric Cancès, Isabelle Catto, Yousra Gati. Mathematical analysis of a nonlinear parabolic equation arising in the modelling of non-newtonian flows. SIAM Journal on Mathematical Analysis, 2005, 37, pp.60-82. ⟨10.1137/S0036141003430044⟩. ⟨hal-00122447⟩