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

Eric Cancès·Isabelle Catto·Yousra Gati
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Abstract

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.

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Eric Cancès, Isabelle Catto, Yousra Gati. 2003-06-06. Mathematical analysis of a nonlinear parabolic equation arising in the modelling of non-newtonian flows. https://arxiv.org/abs/math/0305408

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