Singular limit problem for the two-dimensional Keller-Segel system in scaling critical space

DOI10.1016/j.jde.2020.06.012zbMath1443.35070OpenAlexW3036198238MaRDI QIDQ778242

Takayoshi Ogawa, Masaki Kurokiba

Publication date: 2 July 2020

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

Full work available at URL: https://doi.org/10.1016/j.jde.2020.06.012

zbMATH Keywords

maximal regularityKeller-Segel systemsingular limit probleminitial layer

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Initial value problems for second-order parabolic equations (35K15) Initial value problems for second-order parabolic systems (35K45)

Related Items

Maximal regularity of the heat evolution equation on spatial local spaces and application to a singular limit problem of the Keller-Segel system ⋮ Singular limit problem for the Keller-Segel system and drift-diffusion system in scaling critical Besov-Morrey spaces ⋮ The singular convergence of a chemotaxis-fluid system modeling coral fertilization ⋮ Traveling pulse solutions of a generalized Keller-Segel system with small cell diffusion via a geometric approach ⋮ Maximal regularity and a singular limit problem for the Patlak-Keller-Segel system in the scaling critical space involving \textit{BMO} ⋮ Local well-posedness and finite time blow-up of solutions to an attraction-repulsion chemotaxis system in higher dimensions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• End-point maximal \(L^1\)-regularity for the Cauchy problem to a parabolic equation with variable coefficients
• Finite time blow up for a solution to system of the drift-diffusion equations in higher dimensions
• Small solutions for nonlinear heat equations, the Navier-Stokes equation and the Keller-segel system in Besov and Triebel-Lizorkin spaces
• Global existence for the Cauchy problem of the parabolic-parabolic Keller-Segel system on the plane
• Small data in an optimal Banach space for the parabolic-parabolic and parabolic-elliptic Keller-Segel equations in the whole space
• Existence and uniqueness theorem on weak solutions to the parabolic-elliptic Keller-Segel system
• Global well-posedness for Keller-Segel system in Besov type spaces
• Initiation of slime mold aggregation viewed as an instability
• End-point maximal regularity and its application to two-dimensional Keller-Segel system
• Global solutions of some chemotaxis and angiogenesis system in high space dimension
• The drift-diffusion system in two-dimensional critical Hardy space
• Blowup in infinite time of radial solutions for a parabolic-elliptic system in high-dimensional Euclidean spaces
• Sommes d'opérateurs linéaires et équations différentielles opérationnelles
• On the evolution of self-interacting clusters and applications to semilinear equations with exponential nonlinearity
• Finite time blow-up of the solution for a nonlinear parabolic equation of drift-diffusion type.
• On the closedness of the sum of two closed operators
• A nonlocal singular parabolic problem modelling gravitational interaction of particles
• Singular limit problem for the Keller-Segel system and drift-diffusion system in scaling critical spaces
• Existence, uniqueness and asymptotic behavior of the solutions to the fully parabolic Keller-Segel system in the plane
• Local and global solvability and blow up for the drift-diffusion equation with the fractional dissipation in the critical space
• The uniform boundedness and threshold for the global existence of the radial solution to a drift-diffusion system
• Well-posedness for the drift-diffusion system in \(L^p\) arising from the semiconductor device simulation
• Global Existence of Solutions to a Parabolic-Elliptic System of Drift-Diffusion Type in <b><i>R</i></b>²
• Random walk with persistence and external bias
• BREZIS–MERLE INEQUALITIES AND APPLICATION TO THE GLOBAL EXISTENCE OF THE CAUCHY PROBLEM OF THE KELLER–SEGEL SYSTEM
• Blowup Behavior of Radial Solutions to Jaeger-Luckhaus System in High Dimensional Domains
• Non-uniform bound and finite time blow up for solutions to a drift–diffusion equation in higher dimensions
• The one-dimensional Keller–Segel model with fractional diffusion of cells
• On the parabolic-elliptic limit of the doubly parabolic Keller–Segel system modelling chemotaxis
• On Explosions of Solutions to a System of Partial Differential Equations Modelling Chemotaxis
• Existence and nonexistence of solutions for a model of gravitational interaction of particles, I
• Heat kernels and maximal l^p—l^qestimates for parabolic evolution equations
• Existence and nonexistence of solutions for a model of gravitational interaction of particles, III
• QUALITATIVE BEHAVIOR OF SOLUTIONS OF A DEGENERATE NONLINEAR DRIFT-DIFFUSION MODEL FOR SEMICONDUCTORS
• Well-Posedness in Critical Spaces for Barotropic Viscous Fluids with Truly Not Constant Density
• An Initial Value Problem from Semiconductor Device Theory
• Chemotactic collapse in a parabolic system of mathematical biology
• Blowup of nonradial solutions to parabolic-elliptic systems modeling chemotaxis in two-dimensional domains