Advances in Differential Equations
- Adv. Differential Equations
- Volume 16, Number 9/10 (2011), 937-954.
On the well posedness of a class of PDEs including porous medium and chemotaxis effect
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.
Adv. Differential Equations, Volume 16, Number 9/10 (2011), 937-954.
First available in Project Euclid: 17 December 2012
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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