Some free boundary problems involving non-local diffusion and aggregation
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Publication:2955790
DOI10.1098/rsta.2014.0275zbMath1353.35320arXiv1501.04320OpenAlexW1944799328WikidataQ42512774 ScholiaQ42512774MaRDI QIDQ2955790
Juan Luis Vazquez, José Antonio Carrillo
Publication date: 13 January 2017
Published in: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1501.04320
General theory of partial differential operators (47F05) Free boundary problems for PDEs (35R35) Fourier integral operators applied to PDEs (35S30) Fractional partial differential equations (35R11)
Related Items (10)
An inverse boundary value problem for a two-dimensional pseudo-parabolic equation of third order ⋮ Modeling opinion dynamics: theoretical analysis and continuous approximation ⋮ Geometry of minimizers for the interaction energy with mildly repulsive potentials ⋮ Localization and vector spherical harmonics ⋮ Discrete minimisers are close to continuum minimisers for the interaction energy ⋮ Uniqueness of stationary states for singular Keller-Segel type models ⋮ Explicit equilibrium solutions for the aggregation equation with power-law potentials ⋮ Nonlocal diffusion second order partial differential equations ⋮ The ellipse law: Kirchhoff meets dislocations ⋮ Determination of a time-dependent free boundary in a two-dimensional parabolic problem
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Existence, uniqueness and asymptotic behaviour for fractional porous medium equations on bounded domains
- Regularity of local minimizers of the interaction energy via obstacle problems
- Regularity of solutions of the fractional porous medium flow
- Dimensionality of local minimizers of the interaction energy
- A mass-transportation approach to a one dimensional fluid mechanics model with nonlocal velocity
- Hitchhiker's guide to the fractional Sobolev spaces
- Exponential convergence towards stationary states for the 1D porous medium equation with fractional pressure
- First-order global asymptotics for confined particles with singular pair repulsion
- Confinement for repulsive-attractive kernels
- Entropy solution theory for fractional degenerate convection-diffusion equations
- Barenblatt profiles for a nonlocal porous medium equation
- A fractional porous medium equation
- Nonlinear diffusion of dislocation density and self-similar solutions
- Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations
- Confinement in nonlocal interaction equations
- Nonlinear porous medium flow with fractional potential pressure
- Contractions in the 2-Wasserstein length space and thermalization of granular media
- On minimizers of interaction functionals with competing attractive and repulsive potentials
- A priori estimates for integro-differential operators with measurable kernels
- Double milling in self-propelled swarms from kinetic theory
- Heat kernel estimates for the Dirichlet fractional Laplacian
- The obstacle problem revisited
- On the hydrodynamic limit of Ginzburg-Landau vortices.
- On Maxwellian equilibria of insulated semiconductors
- Limiting embedding theorems for \(W^{s,p}\) when \(s\uparrow 1\) and applications
- Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates
- Evolution of the distribution of wealth in an economic environment driven by local Nash equilibria
- Transformations of self-similar solutions for porous medium equations of fractional type
- Existence of ground states of nonlocal-interaction energies
- Existence of compactly supported global minimisers for the interaction energy
- Asymptotic behaviour of a porous medium equation with fractional diffusion
- Recent progress in the theory of nonlinear diffusion with fractional Laplacian operators
- Finite and infinite speed of propagation for porous medium equations with fractional pressure
- Nonlocal interactions by repulsive-attractive potentials: radial ins/stability
- Equilibria of biological aggregations with nonlocal repulsive-attractive interactions
- Quantitative local and global a priori estimates for fractional nonlinear diffusion equations
- A mean field equation as limit of nonlinear diffusions with fractional Laplacian operators
- Symmetrization for linear and nonlinear fractional parabolic equations of porous medium type
- Barenblatt solutions and asymptotic behaviour for a nonlinear fractional heat equation of porous medium type
- Classical solutions for a logarithmic fractional diffusion equation
- Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian
- Nonlinear stability of flock solutions in second-order swarming models
- THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
- On the spectrum of two different fractional operators
- AGGREGATION AND SPREADING VIA THE NEWTONIAN POTENTIAL: THE DYNAMICS OF PATCH SOLUTIONS
- From the long jump random walk to the fractional Laplacian
- A General Fractional Porous Medium Equation
- Nonlinear Diffusion with Fractional Laplacian Operators
- From Nash to Cournot–Nash equilibria via the Monge–Kantorovich problem
- On global minimizers of repulsive–attractive power-law interaction energies
- A Primer of Swarm Equilibria
- Lp theory for the multidimensional aggregation equation
- Swarm dynamics and equilibria for a nonlocal aggregation model
- Stability Analysis of Flock and Mill Rings for Second Order Models in Swarming
- First Passage Times for Symmetric Stable Processes in Space
- Some Theorems on Stable Processes
- Regularity of the obstacle problem for a fractional power of the laplace operator
- A gradient flow approach to an evolution problem arising in superconductivity
- Blow-up in multidimensional aggregation equations with mildly singular interaction kernels
- Lévy Processes and Stochastic Calculus
- Sharp results for the regularity and stability of the free boundary in the obstacle problem
- Financial Modelling with Jump Processes
- A mean-field model of superconducting vortices
- A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure
- An Extension Problem Related to the Fractional Laplacian
- Explicit Barenblatt profiles for fractional porous medium equations
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