Mathematical analysis of a nonlinear parabolic equation arising in the modelling of non-newtonian flows
Catto, Isabelle; Cancès, Eric; Gati, Yousra (2005), Mathematical analysis of a nonlinear parabolic equation arising in the modelling of non-newtonian flows, SIAM Journal on Mathematical Analysis, 37, 1, p. 60-82. http://dx.doi.org/10.1137/S0036141003430044
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00278227/en/
Journal nameSIAM Journal on Mathematical Analysis
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Abstract (EN)The mathematical properties of a nonlinear parabolic equation arising in the modelling of concentrated suspension 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. The present article is the theoretical side of a joint project with rheologists, aiming at better understanding the flows of complex fluids.
Subjects / Keywordscomplex fluids; nonlinear parabolic equation
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