Phase Transitions and Bump Solutions of the Keller--Segel Model with Volume Exclusion
José A. Carrillo, Xinfu Chen, Qi Wang, Zhi‐An Wang, Lu Zhang
Abstract
We show that the Keller-Segel model in one dimension with Neumann boundary conditions and quadratic cellular diffusion has an intricate phase transition diagram depending on the chemosensitivity strength. Explicit computations allow us to find a myriad of symmetric and asymmetric stationary states whose stability properties are mostly studied via free energy decreasing numerical schemes. The metastability behavior and staircased free energy decay are also illustrated via these numerical simulations.
Topics & Concepts
MetastabilityQuadratic equationComputationDimension (graph theory)Stability (learning theory)MathematicsPhase transitionBoundary (topology)Von Neumann architectureStatistical physicsNeumann boundary conditionDiffusionPhase diagramPhase (matter)Mathematical analysisPhysicsPure mathematicsGeometryComputer scienceThermodynamicsQuantum mechanicsMachine learningAlgorithmMathematical Biology Tumor GrowthGene Regulatory Network AnalysisAdvanced Mathematical Modeling in Engineering