Advances in Differential Equations

On the well posedness of a class of PDEs including porous medium and chemotaxis effect

Messoud Efendiev and Takasi Senba

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Abstract

In this article we deal with a class of degenerate parabolic systems which exhibit two phenomena: porous medium effects and chemotaxis ones. Such classes of equations arise in the modelling (on the mesoscale) of biomass spreading mechanisms via chemotaxis. Under certain "balance conditions'' on the order of the porous medium degeneracy and the growth of the chemotactic functions, we prove well posedness.

Article information

Source
Adv. Differential Equations Volume 16, Number 9/10 (2011), 937-954.

Dates
First available in Project Euclid: 17 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355703182

Mathematical Reviews number (MathSciNet)
MR2850759

Zentralblatt MATH identifier
1231.35088

Subjects
Primary: 35A05 35K15: Initial value problems for second-order parabolic equations 35K55: Nonlinear parabolic equations 35K55: Nonlinear parabolic equations 35K57: Reaction-diffusion equations 35K65: Degenerate parabolic equations 37L05: General theory, nonlinear semigroups, evolution equations

Citation

Efendiev, Messoud; Senba, Takasi. On the well posedness of a class of PDEs including porous medium and chemotaxis effect. Adv. Differential Equations 16 (2011), no. 9/10, 937--954. https://projecteuclid.org/euclid.ade/1355703182.


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