New Explicit Exact Solutions of the One-Dimensional Parabolic-Parabolic Keller-Segel Model
نویسندگان
چکیده
منابع مشابه
Large mass self-similar solutions of the parabolic-parabolic Keller-Segel model of chemotaxis.
In two space dimensions, the parabolic-parabolic Keller-Segel system shares many properties with the parabolic-elliptic Keller-Segel system. In particular, solutions globally exist in both cases as long as their mass is less than a critical threshold M(c). However, this threshold is not as clear in the parabolic-parabolic case as it is in the parabolic-elliptic case, in which solutions with mas...
متن کاملOn the parabolic-elliptic limit of the doubly parabolic Keller–Segel system modelling chemotaxis
We establish new convergence results, in strong topologies, for solutions of the parabolic-parabolic Keller–Segel system in the plane, to the corresponding solutions of the parabolic-elliptic model, as a physical parameter goes to zero. Our main tools are suitable space-time estimates, implying the global existence of slowly decaying (in general, nonintegrable) solutions for these models, under...
متن کاملA (1 + 2)-Dimensional Simplified Keller-Segel Model: Lie Symmetry and Exact Solutions. II
Abstract: A simplified Keller–Segel model is studied by means of Lie symmetry based approaches. It is shown that a (1 + 2)-dimensional Keller–Segel type system, together with the correctly-specified boundary and/or initial conditions, is invariant with respect to infinite-dimensional Lie algebras. A Lie symmetry classification of the Cauchy problem depending on the initial profile form is prese...
متن کاملAsymptotic estimates for the parabolic-elliptic Keller-Segel model in the plane
We investigate the large-time behavior of the solutions of the two-dimensional Keller-Segel system in self-similar variables, when the total mass is subcritical, that is less than 8π after a proper adimensionalization. It was known from previous works that all solutions converge to stationary solutions, with exponential rate when the mass is small. Here we remove this restriction and show that ...
متن کاملA (1+2)-Dimensional Simplified Keller-Segel Model: Lie Symmetry and Exact Solutions
This research is a natural continuation of the recent paper “Exact solutions of the simplified Keller–Segel model” (Commun Nonlinear Sci Numer Simulat 2013, 18, 2960–2971). It is shown that a (1+2)-dimensional Keller–Segel type system is invariant with respect infinite-dimensional Lie algebra. All possible maximal algebras of invariance of the Neumann boundary value problems based on the Keller...
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ژورنال
عنوان ژورنال: Applied and Computational Mathematics
سال: 2018
ISSN: 2328-5605
DOI: 10.11648/j.acm.20180702.13