Weighted weak formulation for a nonlinear degenerate parabolic equation arising in chemotaxis or porous media

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• 作者：Moustafa Ibrahim ^{Moustafa.Ibrahim@ec-nantes.fr" class="auth_mail" title="E-mail the corresponding author} ; Mazen Saad ; ^{Mazen.Saad@ec-nantes.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Parabolic degenerate equation ; Compactness ; Weak formulation
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：446
• 期：1
• 页码：945-969
• 全文大小：479 K

文摘

This paper is devoted to the mathematical analysis of a degenerate nonlinear parabolic equation. This kind of equations stems either from the modeling of a compressible two phase flow in porous media or from the modeling of a chemotaxis-fluid process. In the degenerate equation, the strong nonlinearities are technically difficult to be controlled by the degenerate dissipative term because the equation itself presents degenerate terms of order 0 and of order 1. In the case of the sub-quadratic degeneracy of the dissipative term at one point, a weak and classical formulation is possible for the expected solutions. However, in the case of the degeneracy of the dissipative term at two points, we obtain solutions in a weaker sense compared to the one of the classical formulation. Therefore, a degenerate weighted formulation is introduced taking into account the degeneracy of the dissipative term.