The behavior of solutions of multidimensional aggregation equations with mildly singular interaction kernels
From MaRDI portal
Publication:964790
DOI10.1007/s11401-009-0191-5zbMath1188.35141OpenAlexW2027481868MaRDI QIDQ964790
Thomas Laurent, Andrea L. Bertozzi
Publication date: 21 April 2010
Published in: Chinese Annals of Mathematics. Series B (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11401-009-0191-5
PDEs in connection with fluid mechanics (35Q35) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Blow-up in context of PDEs (35B44) PDEs in connection with classical thermodynamics and heat transfer (35Q79)
Related Items
Boundary layer analysis from the Keller-Segel system to the aggregation system in one space dimension ⋮ The McKean-Vlasov equation in finite volume ⋮ The aggregation equation with power-law kernels: ill-posedness, mass concentration and similarity solutions ⋮ Biological Aggregation Driven by Social and Environmental Factors: A Nonlocal Model and Its Degenerate Cahn--Hilliard Approximation ⋮ Friction dominated dynamics of interacting particles locally close to a crystallographic lattice ⋮ Optimal control for a mixed flow of Hamiltonian and gradient type in space of probability measures ⋮ Equivalence of gradient flows and entropy solutions for singular nonlocal interaction equations in 1D ⋮ An invariance principle for gradient flows in the space of probability measures ⋮ Stability and clustering of self-similar solutions of aggregation equations
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A nonlocal continuum model for biological aggregation
- Finite-time singularities of an aggregation equation in \(\mathbb R^n\) with fractional dissipation
- Contractions in the 2-Wasserstein length space and thermalization of granular media
- An integro-differential equation arising as a limit of individual cell-based models
- Initiation of slime mold aggregation viewed as an instability
- Uniqueness of the solution to the Vlasov--Poisson system with bounded density
- On a nonlocal aggregation model with nonlinear diffusion
- Finite-time blow-up of \(L^\infty \)-weak solutions of an aggregation equation
- Uniqueness of signed measures solving the continuity equation for Osgood vector fields
- Large time behavior of nonlocal aggregation models with nonlinear diffusion
- Stability of a 4th-order curvature condition arising in optimal transport theory
- Refined blowup criteria and nonsymmetric blowup of an aggregation equation
- A non-local model for a swarm
- A convexity principle for interacting gases
- Modeling the aggregative behavior of ants of the species Polyergus rufescens
- Diffusion and ecological problems: Modern perspectives.
- Optimal critical mass in the two dimensional Keller-Segel model in \(R^2\)
- An interacting particle system modelling aggregation behavior: from individuals to populations
- On spherically symmetric gravitational collapse
- Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates
- Long-time asymptotics of kinetic models of granular flows
- Finite-time blow-up of solutions of an aggregation equation in \(\mathbb R^n\)
- On an aggregation model with long and short range interactions
- Existence of solutions to degenerate parabolic equations via the Monge-Kantorovich theory
- Formation of clumps and patches in self-aggregation of finite-size particles
- One-dimensional kinetic models of granular flows
- THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
- Random walk with persistence and external bias
- Lp theory for the multidimensional aggregation equation
- Infinite time aggregation for the critical Patlak‐Keller‐Segel model in ℝ2
- Blow-up in multidimensional aggregation equations with mildly singular interaction kernels
- Global and Exploding Solutions for Nonlocal Quadratic Evolution Problems
- Diffusion, attraction and collapse
- Formation of strong fronts in the 2-D quasigeostrophic thermal active scalar
- A kinetic equation for granular media
- The Variational Formulation of the Fokker--Planck Equation
- Existence of Weak Solutions to Some Vortex Density Models
- Swarming Patterns in a Two-Dimensional Kinematic Model for Biological Groups
- Stability analysis of swarms
- Self-Similar Blowup Solutions to an Aggregation Equation in $R^n$
- Local and Global Existence for an Aggregation Equation
