Global strong solution to the semi-linear Keller-Segel system of parabolic-parabolic type with small data in scale invariant spaces

DOI10.1016/j.jde.2009.03.027zbMath1207.35178OpenAlexW2007066174MaRDI QIDQ1022319

Yoshie Sugiyama, Hideo Kozono

Publication date: 10 June 2009

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2009.03.027

Mathematics Subject Classification ID

Initial value problems for second-order parabolic systems (35K45) Cell movement (chemotaxis, etc.) (92C17) Semilinear parabolic equations (35K58)

Related Items (27)

Suppression of blow-up in parabolic–parabolic Patlak–Keller–Segel via strictly monotone shear flows ⋮ Global well-posedness for nonlocal fractional Keller-Segel systems in critical Besov spaces ⋮ Ill-posedness of the two-dimensional Keller-Segel model in Triebel-Lizorkin spaces ⋮ On the fractional doubly parabolic Keller-Segel system modelling chemotaxis ⋮ Global existence of solutions to a parabolic-parabolic system for chemotaxis with weak degradation ⋮ Maximal regularity of the heat evolution equation on spatial local spaces and application to a singular limit problem of the Keller-Segel system ⋮ On the Neumann problem for fractional semilinear elliptic equations arising from Keller–Segel model ⋮ Strong periodic solutions to quasilinear parabolic equations: An approach by the Da Prato–Grisvard theorem ⋮ Existence and uniqueness theorem on mild solutions to the Keller-Segel system coupled with the Navier-Stokes fluid ⋮ Dynamics in two-predator and one-prey models with signal-dependent motility ⋮ Existence and Gevrey regularity for a two-species chemotaxis system in homogeneous Besov spaces ⋮ Existence and uniqueness theorem on mild solutions to the Keller-Segel system in the scaling invariant space ⋮ Global existence of weak solutions to quasilinear degenerate Keller-Segel systems of parabolic-parabolic type ⋮ Global existence and time decay estimate of solutions to the Keller–Segel system ⋮ Blow-up profiles for a semilinear chemotaxis system arising in biology ⋮ Global existence of weak solutions to quasilinear degenerate Keller-Segel systems of parabolic-parabolic type with small data ⋮ Strong solutions to the Keller-Segel system with the weakL^n/2initial data and its application to the blow-up rate ⋮ Strong time periodic solutions to Keller-Segel systems: an approach by the quasilinear Arendt-Bu theorem ⋮ Global existence and large time behavior of a 2D Keller-Segel system in logarithmic Lebesgue spaces ⋮ On a generalized doubly parabolic Keller–Segel system in one spatial dimension ⋮ Keller-Segel chemotaxis models: a review ⋮ Preface ⋮ The Keller-Segel system of parabolic-parabolic type in homogeneous Besov spaces framework ⋮ Multi-species Patlak-Keller-Segel system ⋮ Global well-posedness and asymptotic behavior in Besov-Morrey spaces for chemotaxis-Navier-Stokes fluids ⋮ The Keller-Segel system on bounded convex domains in critical spaces ⋮ Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues

Cites Work

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• Time global existence and asymptotic behavior of solutions to generate quasi-linear parabolic systems of chemotaxis.
• Blow-up criterion via scaling invariant quantities with effect on coefficient growth in Keller-Segel system.
• Chemotactic collapse for the Keller-Segel model
• Dynamic theory of quasilinear parabolic equations. II: Reaction-diffusion systems
• Initiation of slime mold aggregation viewed as an instability
• Global solutions of some chemotaxis and angiogenesis system in high space dimension
• Local existence and finite time blow-up of solutions in the 2-D Keller-Segel system
• The parabolic-parabolic Keller-Segel model in \(\mathbb R^2\)
• Nonlinear aspects of chemotaxis
• Remarks on the preceding paper by M. Ben-Artzi ``Global solutions of two- dimensional Navier-Stokes and Euler equations
• Asymptotic decay for the solutions of the parabolic-parabolic Keller-Segel chemotaxis system in critical spaces
• Critical space for the parabolic-parabolic Keller--Segel model in \(\mathbb R^{d}\)
• Global existence and decay properties for a degenerate Keller-Segel model with a power factor in drift term
• Singularity patterns in a chemotaxis model
• Large time behavior of solutions in super-critical cases to degenerate Keller-Segel systems
• The Keller-Segel system of parabolic-parabolic type with initial data in weak $L^{n/2}(\mathbb{R}^n)$ and its application to self-similar solutions
• On Explosions of Solutions to a System of Partial Differential Equations Modelling Chemotaxis
• Decay Properties and Asymptotic Profiles of Bounded Solutions to a Parabolic System of Chemotaxis in Rn
• Asymptotic profile with the optimal convergence rate for a parabolic equation of chemotaxis in super-critical cases
• Blowup of nonradial solutions to parabolic-elliptic systems modeling chemotaxis in two-dimensional domains

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