Article
Mathematics
Jaewook Ahn, Kyungkeun Kang, Jihoon Lee
Summary: The passage discusses a class of logarithmic Keller-Segel type systems modeling the spatio-temporal behavior of chemotactic cells or criminal activities in spatial dimensions two and higher. It establishes the existence of classical solutions globally in time under certain assumptions on parameter values and given functions. The text also introduces a new type of small initial data to obtain global classical solutions and discusses the long-time asymptotic behaviors of solutions.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics, Applied
Qiang Hua, Qian Zhang
Summary: In this paper, we investigate the Cauchy problem for the three-dimensional incompressible Keller-Segel-Navier-Stokes equations and establish the global well-posedness for the system by leveraging the geometry of axisymmetric flow without swirl.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2021)
Article
Mathematics, Applied
Joelma Azevedo, Mario Bezerra, Claudio Cuevas, Herme Soto
Summary: This paper analyzes the time-fractional Keller-Segel system in a new framework and derives the global well-posedness and asymptotic behavior of solutions in critical Besov-weak-Herz spaces.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics
Masterson Costa, Claudio Cuevas, Clessius Silva, Herme Soto
Summary: This work studies the well-posedness and blow-up problems of the time-fractional Keller-Segel model in Lebesgue and Besov spaces under homogeneous Neumann boundary conditions in a smooth domain of R-N. The KS model is a coupled system of partial differential equations. Additionally, this paper also investigates the unique continuation of the solution and the continuous dependence on the initial data for the continued solution.
MATHEMATISCHE NACHRICHTEN
(2023)
Article
Mathematics, Applied
Shuofa Xiao, Haiyan Xu
Summary: In this paper, we investigate the singular limit problem of a Keller-Segel-Navier-Stokes system with two nonlinear terms on the torus T-n. By utilizing the properties of the heat kernel, we obtain the generalized maximal regularity estimates and solve this singular limit problem by combining the Banach fixed-point theorem.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Xiang Fei, Yanghai Yu, Mingwen Fei
Summary: In this paper, we present a new construction that satisfies u(0)∈(σ)(B)(p,∞), indicating that the corresponding solution to the hyperbolic Keller-Segel model from u(0) exhibits a discontinuity at t = 0 in the metric of B-p,∞(σ)(R-d). This implies the ill-posedness of this equation in B-p,∞(σ). Our result extends the recent work by Zhang et al. (J Differ Equ 334:451-489, 2022) where the case d = 1 and p = 2 was studied.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2023)
Article
Mathematics, Applied
Hui Huang, Jinniao Qiu
Summary: In this paper, a stochastic aggregation-diffusion equation of the Keller-Segel type for modeling chemotaxis in dimensions 2 and 3 is proposed and studied. Unlike the classical deterministic KS system, the stochastic KS equation considers both idiosyncratic and common noises in an interacting particle system. The unique existence of solutions to the stochastic KS equation and the mean-field limit result are addressed.
JOURNAL OF NONLINEAR SCIENCE
(2021)
Article
Mathematics
Elisabetta Rocca, Giulio Schimperna, Andrea Signori
Summary: This study proposes a new type of diffuse interface model that describes the evolution of a tumor mass under the effects of a chemical substance. The model combines the Cahn-Hilliard equation with a subsystem of the Keller-Segel model, resulting in more effective capturing of chemotactic effects in tumor growth dynamics. The study provides mathematical proofs for the existence of weak solutions and uniqueness and continuous dependence of smooth solutions in significant cases.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics
Taiki Takeuchi
Summary: We investigate the local well-posedness of the Keller-Segel-Navier-Stokes system with initial data in the scaling invariant Besov spaces, where the solution exists globally in time if the initial data is sufficiently small. We also find that the solution belongs to the Lorentz spaces in the time direction and is smooth in space and time. Additionally, we obtain the maximal regularity estimates of solutions under certain conditions. Furthermore, we show that the solution has additional regularities if the initial data has higher regularities. This implies that global solutions decay as the limit t -> infinity in the same norm of the space of the initial data. Our results on the Lorentz regularity estimates are based on the strategy by Kozono-Shimizu (2019) [26].
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics, Applied
Takeshi Suguro
Summary: In this paper, the well-posedness of the Keller-Segel system in uniformly local Lebesgue spaces is considered, along with the unconditional uniqueness of mild solutions and the uniformly local almost periodicity of these solutions. The study focuses on using only local properties of the initial data to analyze the parabolic-elliptic Keller-Segel system involving a nonlocal term.
JOURNAL OF EVOLUTION EQUATIONS
(2021)
Article
Mathematics
Lei Zhang, Chunlai Mu, Shouming Zhou
Summary: In this paper, the discontinuity of the solution map for the one-dimensional hyperbolic Keller-Segel equations (HKSE) is shown by constructing special initial data. The Hadamard local well-posedness result for the high dimensional HKSE is established in larger Besov spaces, improving the local theory. The inviscid limit of the Keller-Segel equations with small diffusivity is investigated, and two blow-up criteria for strong solutions in Besov spaces are established using the Littlewood-Paley theory.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics
Shouming Zhou, Simin Zhang, Chunlai Mu
Summary: This paper investigates the local well-posedness for the Cauchy problem of the hyperbolic Keller Segel equation in Besov spaces, obtaining results on local existence, uniqueness, and continuous dependence on initial data. It further shows that the data-to-solution map is not uniformly continuous in these Besov spaces.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Biochemical Research Methods
Leon Avery, Brian Ingalls, Catherine Dumur, Alexander Artyukhin
Summary: Collective behaviors in Starved first-stage larvae of the nematode Caenorhabditis elegans are known to produce large-scale organization. A mathematical model was developed to explain how and why the larvae aggregate, focusing on chemotaxis and the role of two chemical signals. Knocking out the sensory receptor gene srh-2 resulted in irregularly shaped aggregates, suggesting that mutant worms moved slower than wild type.
PLOS COMPUTATIONAL BIOLOGY
(2021)
Article
Mathematics, Applied
Miaochao Chen, Shengqi Lu, Qilin Liu
Summary: This paper proves uniqueness results of weak solutions to a Keller-Segel-Navier-Stokes system in a bounded domain Omega subset of R-N (N >= 3) under certain conditions, and also shows that these conditions hold true when N = 2 for the system with a logistic term.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Applied
Jason J. Bramburger
Summary: In this study, a Keller-Segel model with logistic growth dynamics is presented for the study of chemotactic pattern formation. The existence of a minimum wave speed is proven, where the model exhibits nonnegative traveling wave solutions above this speed and none below. The exact value of the minimum wave speed is provided for all biologically relevant parameter values, strengthening recent results in a restricted parameter regime.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Developmental Biology
Cristobal Quininao, Alain Prochiantz, Jonathan Touboul
Article
Mathematics, Applied
Benoit Perthame, Cristobal Quininao, Jonathan Touboul
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2015)
Review
Mathematical & Computational Biology
Patricio Cumsille, Anibal Coronel, Carlos Conca, Cristobal Quininao, Carlos Escudero
THEORETICAL BIOLOGY AND MEDICAL MODELLING
(2015)
Article
Mathematics, Applied
Cristobal Quininao
ACTA APPLICANDAE MATHEMATICAE
(2016)
Article
Physics, Mathematical
S. Mischler, C. Quininao, J. Touboul
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2016)
Article
Biology
V. P. Weinberger, C. Quininao, P. A. Marquet
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY B-BIOLOGICAL SCIENCES
(2017)
Article
Mathematics, Applied
Cristobal Quininao, Jonathan Touboul
ACTA APPLICANDAE MATHEMATICAE
(2015)
Article
Physics, Mathematical
S. Mischler, C. Quininao, Q. Weng
JOURNAL OF STATISTICAL PHYSICS
(2018)
Article
Ecology
Mauricio Tejo, Cristobal Quininao, Rolando Rebolledo, Pablo A. Marquet
Summary: This study introduces a stochastic model to investigate the competition/colonization trade-off as a coexistence mechanism in metacommunities. The model shows that the balance between competition and colonization intensity is influenced by the number of local communities and refuges for inferior competitors. The results emphasize the role of topology and dispersal in affecting competition outcomes in local communities.
THEORETICAL ECOLOGY
(2021)
Article
Multidisciplinary Sciences
Vicente Salinas, Cristobal Quininao, Sebastian Gonzalez, Gustavo Castillo
Summary: This study investigates the role of small-scale perturbations in the onset of avalanches in a rotating drum in the stick-slip regime. It shows that the order parameter describing the system is kinetic energy and that the onset of avalanche is determined by oscillation amplitude for high frequencies. A theoretical model is presented to explain the transition between continuous and discrete avalanche regimes as a supercritical Hopf bifurcation.
SCIENTIFIC REPORTS
(2021)
Article
Mathematics, Applied
Pedro Perez-Aros, Cristobal Quininao, Mauricio Tejo
Summary: This paper addresses a control optimization problem involving stochastic dynamics, where the dynamic is discretized and the space of control functions is restricted to piecewise mappings. The results are illustrated through numerical simulations considering classical models for population growth.
APPLIED MATHEMATICS AND OPTIMIZATION
(2022)
Article
Mathematics, Applied
Cristobal Quininao, Jonathan D. Touboul
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
(2020)
