Global solutions in a fully parabolic chemotaxis system with singular sensitivity

By Michael Winkler. 2011

245 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Modeling and Simulation, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/93cb6ada9594dd464b2565c1b76e3b82056df1b0

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Citations in the corpus

Mathematics of traveling waves in chemotaxis --Review paper-- (2012, background): “The steady states for the logarithmic sensitivity with f(u, v) = u−v was studied in [52, 61] and existence of global solutions was recently obtained in [86].”
A new approach toward boundedness in a two‐dimensional parabolic chemotaxis system with singular sensitivity (2015, background): “In [10], also weak solutions have been shown to exist for Equation (1), as long as < q nC2 3n 4 .”
A critical blow-up exponent in a chemotaxis system with nonlinear signal production (2018, background): “1) upon replacing the first equation therein with ut = ∆u − χ∇ · ( v∇v), the size of the parameter χ is known to play a crucial role with regard to the occurrence of blow-up: on the one hand, exclusively global smooth solutions exist if n 2 and χ < χ (n) with some χ (n) ∈ (0,∞] depending on whether”
A generalized solution concept for the Keller–Segel system with logarithmic sensitivity: global solvability for large nonradial data (2017, methodology): “2), as already used in a slightly modified form and for more restricted choices of χ in [21].”
Depleting the signal: Analysis of chemotaxis‐consumption models—A survey (2023, unknown): “also [140] for a precedent), namely, for suitably chosen p > 1, δ > 0 and φ : [0, δ] → (0,∞), the expressions F2(t) := ∫”
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”
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”
The two-dimensional Keller–Segel system with singular sensitivity and signal absorption: Global large-data solutions and their relaxation properties (2016, background): “2) the signal production mechanism expressed in the second equation is known to inhibit an evolution of v toward small values in such an effective manner that global existence of bounded smooth solutions can be achieved for reasonably smooth but arbitrarily large data in initial-boundary value probl”
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 ”
Boundedness of solutions to parabolic–elliptic Keller–Segel systems with signal‐dependent sensitivity (2015, background): “On the other hand, in [14], the global existence of classical solutions to (1.”