Decay Properties and Asymptotic Profiles of Bounded Solutions to a Parabolic System of Chemotaxis in Rn

DOI10.1619/fesi.46.383zbMath1330.35476OpenAlexW2069854284MaRDI QIDQ4824366

Rai Syukuinn, Toshitaka Nagai, Masayuki Umesako

Publication date: 1 November 2004

Published in: Funkcialaj Ekvacioj (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1619/fesi.46.383

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Population dynamics (general) (92D25) Initial value problems for second-order parabolic systems (35K45)

Related Items (39)

The pointwise estimates of solutions to the Cauchy problem of a chemotaxis model ⋮ Asymptotic expansion of solutions to the drift-diffusion equation with fractional dissipation ⋮ Persistence and convergence in parabolic-parabolic chemotaxis system with logistic source on \(\mathbb{R}^N\) ⋮ Large time behavior of bounded solutions to a parabolic system of chemotaxis in the whole space ⋮ ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO DRIFT-DIFFUSION SYSTEM WITH GENERALIZED DISSIPATION ⋮ On the fractional doubly parabolic Keller-Segel system modelling chemotaxis ⋮ The flux limited Keller-Segel system; properties and derivation from kinetic equations ⋮ Asymptotic expansions of solutions of the Cauchy problem for nonlinear parabolic equations ⋮ Spreading speeds of a parabolic-parabolic chemotaxis model with logistic source on \(\mathbb{R}^N\) ⋮ Large time behavior of solutions to the 3D anisotropic Navier-Stokes equation ⋮ Asymptotic behaviour in a one dimensional model of interacting particles ⋮ Global solution of the chemotaxis attraction-repulsion Cauchy problem with the nonlinear signal production in \(\mathbb{R}^N\) ⋮ Asymptotic decay for the solutions of the parabolic-parabolic Keller-Segel chemotaxis system in critical spaces ⋮ Large time behavior of classical solutions to a fractional attraction–repulsion Keller–Segel system in the whole space ⋮ Strong solutions to a nonlinear stochastic aggregation-diffusion equation ⋮ Convergence to diffusion waves for solutions of 1D Keller–Segel model ⋮ Well‐posedness and blow‐up of the fractional Keller–Segel model on domains ⋮ 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 ⋮ Well-posedness for a model derived from an attraction-repulsion chemotaxis system ⋮ Asymptotic behavior of solutions of a model derived from the 1‐D Keller–Segel model on the half line ⋮ Diffusion-dominated asymptotics of solution to chemotaxis model ⋮ Green's function of a chemotaxis model in the half space and its applications ⋮ Global existence and asymptotic properties of the solution to a two-species chemotaxis system ⋮ Large time behavior of the full attraction-repulsion Keller-Segel system in the whole space ⋮ Boundedness of solutions to a parabolic attraction-repulsion chemotaxis system in \(\mathbb{R}^2\): the attractive dominant case ⋮ Existence, uniqueness and asymptotic behavior of the solutions to the fully parabolic Keller-Segel system in the plane ⋮ Critical space for the parabolic-parabolic Keller--Segel model in \(\mathbb R^{d}\) ⋮ Asymptotic expansion of solutions to the drift-diffusion equation with large initial data ⋮ Asymptotic behavior of a solution to the drift-diffusion equation for a fast-diffusion case ⋮ Global strong solution to the semi-linear Keller-Segel system of parabolic-parabolic type with small data in scale invariant spaces ⋮ Improvement of convergence rates for a parabolic system of chemotaxis in the whole space ⋮ Asymptotic behaviour for small mass in the two-dimensional parabolic-elliptic Keller-Segel model ⋮ Global existence and boundedness of solutions to a parabolic attraction-repulsion chemotaxis system in \(\mathbb{R}^2\): the repulsive dominant case ⋮ Large time behavior of solutions in super-critical cases to degenerate Keller-Segel systems ⋮ Asymptotic expansion of solutions to the nonlinear dissipative equation with the anomalous diffusion ⋮ Global solutions for the critical Burgers equation in the Besov spaces and the large time behavior ⋮ An iterative approach to \(L^\infty\)-boundedness in quasilinear Keller-Segel systems

This page was built for publication: Decay Properties and Asymptotic Profiles of Bounded Solutions to a Parabolic System of Chemotaxis in Rn