Longtime dynamics of the PDE model for the motion toward light of bacterial colonies

DOI10.1088/1361-6544/aa999dzbMath1384.92016OpenAlexW2791224410MaRDI QIDQ4635058

Marina Chugunova, Roman M. Taranets

Publication date: 13 April 2018

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/1361-6544/aa999d

zbMATH Keywords

stability analysisexistence of weak solutionssteady stateslongtime dynamicsphototaxis modeling

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Initial value problems for higher-order parabolic equations (35K30) Cell movement (chemotaxis, etc.) (92C17) Higher-order parabolic equations (35K25)

Cites Work

• A nonlocal continuum model for biological aggregation
• Existence and long-time behaviour of weak solutions for the Mullins equation
• Model for chemotaxis
• On generalized Csiszár-Kullback inequalities
• Mutual interactions, potentials, and individual distance in a social aggregation
• Stochastic models for phototaxis
• Bifurcating spatially heterogeneous solutions in a chemotaxis model for biological pattern generation
• Continuum modeling of the equilibrium and stability of animal flocks
• Modeling local interactions during the motion of cyanobacteria
• A local PDE model of aggregation formation in bacterial colonies
• Modeling selective local interactions with memory: Motion on a 2D lattice
• Swarm dynamics and equilibria for a nonlocal aggregation model
• Classical solutions and pattern formation for a volume filling chemotaxis model
• Swarming Patterns in a Two-Dimensional Kinematic Model for Biological Groups
• Nonnegative Weak Solutions for a Degenerate System Modeling the Spreading of Surfactant on Thin Films
• The stability of spike solutions to the one-dimensional Gierer-Meinhardt model

This page was built for publication: Longtime dynamics of the PDE model for the motion toward light of bacterial colonies