Global weak solutions in a chemotaxis system with large singular sensitivity

By Christian Stinner, Michael Winkler. 2011

137 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/d4420a86a99965dd1c82455a6758fbcd3ba6a2c1

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In Applied Mathematics

In Computational Theory and Mathematics

In Modeling and Simulation

Citations in the corpus

Analysis of a chemotaxis model with indirect signal absorption (2019, background): “4) have also already been studied with p ∈ (0, 1) in [11, 18], in both cases with φ(s) = s, s ≥ 0, for some q > 0.”
Effects of signal-dependent motilities in a Keller–Segel-type reaction–diffusion system (2017, result): “1) seems complex enough so as to allow for partial results identifying conditions sufficient for global boundedness up to now, with an exception formed by the particular choice χ(v) = χ0 v of a singular sensitivity consistent with the Weber-Fechner law for which besides various results on global sol”
A new approach toward boundedness in a two‐dimensional parabolic chemotaxis system with singular sensitivity (2015, background): “In the radially symmetric setting, moreover, certain global weak ‘power- -solutions’ exist ([12]).”
The two-dimensional Keller–Segel system with singular sensitivity and signal absorption: Global large-data solutions and their relaxation properties (2016, background): “Within larger ranges of χ, at least weak solutions exist globally ([44]), where in the two-dimensional radially symmetric case certain generalized solutions can be constructed actually without any restriction on the size of χ ([37]).”
Boundedness of solutions to parabolic–elliptic Keller–Segel systems with signal‐dependent sensitivity (2015, background): “Later, in [15], certain weak solutions to (1.”
Locally bounded global solutions to a chemotaxis consumption model with singular sensitivity and nonlinear diffusion (2016, background): “(For this system, global solutions are known to exist if χ is sufficiently small, where the precise condition depends on the dimension as well as on whether classical ([17, 40, 4]) or weak solutions ([34, 40]) are considered and on radial symmetry of initial data ([4, 28]); but for large χ also blow”
A generalized solution concept for the Keller–Segel system with logarithmic sensitivity: global solvability for large nonradial data (2017, background): “This idea has partially been adapted to the present context in [17] already, but in the present work we shall further weaken the requirements on solutions to a considerable extent: Namely, for the crucial first sub-problem (1.”
LARGE-TIME BEHAVIOR OF A PARABOLIC-PARABOLIC CHEMOTAXIS MODEL WITH LOGARITHMIC SENSITIVITY IN ONE DIMENSION (2012, background): “Before concluding this section, we should mention some works on attraction chemotaxis models with logarithmic sensitivity but with linear chemical production and degradation g(u, v) := u − v: all classical solutions are global in time when n = 1 [29], or when n = 2 and χ > 0 is small [3], or when n ”