Fetching the paper…
Reading the bibliography…
As a counterpoint to classical stochastic particle methods for diffusion, we develop a deterministic particle method for linear and nonlinear diffusion.
QUADPACK: a Subroutine Package for Automatic Integration
R. Piessens, E. de Doncker-Kapenga, C. W. Überhuber, and D. K. Kahaner · 1983
Earlier work this paper cites.
Particle methods for the one-dimensional Vlasov–Poisson equations
G.-H. Cottet and P.-A. Raviart · 1984
Earlier work this paper cites.
On vortex methods
C. Anderson and C. Greengard · 1985
Earlier work this paper cites.
The weighted particle method for convection-diffusion equations. I. The case of an isotropic viscosity
P. Degond and S. Mas-Gallic · 1989
Earlier work this paper cites.
The weighted particle method for convection-diffusion equations. II. The anisotropic case
P. Degond and S. Mas-Gallic · 1989
Earlier work this paper cites.
A deterministic approximation of diffusion equations using particles
P. Degond and F.-J. Mustieles · 1990
Earlier work this paper cites.
Convergence of the point vortex method for the 2 2 -D Euler equations
J. Goodman, T. Y. Hou, and J. Lowengrub · 1990
Earlier work this paper cites.
Large systems of interacting particles and the porous medium equation
K. Oelschläger · 1990
Earlier work this paper cites.
Functional Analysis
F. Riesz and B. Sz.-Nagy · 1990
Earlier work this paper cites.
Deterministic diffusion of particles
G. Russo · 1990
Earlier work this paper cites.
A particle method for collisional kinetic equations. i. basic theory and one-dimensional results
G. Russo · 1990
Earlier work this paper cites.
A convexity principle for interacting gases
R. J. McCann · 1997
Earlier work this paper cites.
The variational formulation of the Fokker–Planck equation
R. Jordan, D. Kinderlehrer, and F. Otto · 1998
Earlier work this paper cites.
Presentation and analysis of a diffusion-velocity method
G. Lacombe and S. Mas-Gallic · 1999
Earlier work this paper cites.
Vortex methods
G.-H. Cottet and P. D. Koumoutsakos · 2000
Earlier work this paper cites.
SciPy: Open source scientific tools for Python
E. Jones, T. Oliphant, P. Peterson, et al · 2001
Earlier work this paper cites.
Une méthode particulaire déterministe pour des équations diffusives non linéaires
P.-L. Lions and S. Mas-Gallic · 2001
Earlier work this paper cites.
The geometry of dissipative evolution equations: the porous medium equation
F. Otto · 2001
Earlier work this paper cites.
The diffusion velocity method: a deterministic way of moving the nodes for solving diffusion equations
S. Mas-Gallic · 2002
Earlier work this paper cites.
Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates
J. A. Carrillo, R. J. McCann, and C. Villani · 2003
Earlier work this paper cites.
Topics in optimal transportation
C. Villani · 2003
Earlier work this paper cites.
Solution of a model Boltzmann equation via steepest descent in the 2-Wasserstein metric
E. A. Carlen and W. Gangbo · 2004
Earlier work this paper cites.
Optimal critical mass in the two-dimensional Keller–Segel model in ℝ 2 \mathbb{R}^{2}
J. Dolbeault and B. t. Perthame · 2004
Earlier work this paper cites.
Gamma-convergence of gradient flows with applications to Ginzburg–Landau
E. Sandier and S. Serfaty · 2004
Earlier work this paper cites.
Diffeomorphisms and nonlinear heat flows
L. Evans, O. Savin, and W. Gangbo · 2005
Earlier work this paper cites.
Two-dimensional Keller–Segel model: optimal critical mass and qualitative properties of the solutions
A. Blanchet, J. Dolbeault, and B. Perthame · 2006
Earlier work this paper cites.
Two-dimensional Keller–Segel model: optimal critical mass and qualitative properties of the solutions
A. Blanchet, J. Dolbeault, and B. t. Perthame · 2006
Earlier work this paper cites.
Contractions in the 2-Wasserstein length space and thermalization of granular media
J. A. Carrillo, R. J. McCann, and C. Villani · 2006
Cited alongside, same era.
Identification of asymptotic decay to self-similarity for one-dimensional filtration equations
L. Gosse and G. Toscani · 2006
Cited alongside, same era.
Lagrangian numerical approximations to one-dimensional convolution-diffusion equations
L. Gosse and G. Toscani · 2006
Cited alongside, same era.
Gradient flows of probability measures
L. Ambrosio and G. Savaré · 2007
Cited alongside, same era.
Modified Keller–Segel system and critical mass for the log interaction kernel
V. Calvez, B. Perthame, and M. Sharifi tabar · 2007
Cited alongside, same era.
Matplotlib: a 2d graphics environment
J. D. Hunter · 2007
Cited alongside, same era.
Uniqueness for Keller–Segel-type chemotaxis models
J. A. Carrillo, S. Lisini, and E. Mainini · 2014
Later among the works it cites.
Fatou’s lemma for weakly converging probabilities
E. A. Feinberg, P. O. Kasyanov, and N. V. Zadoianchuk · 2014
Later among the works it cites.
A review of the mean field limits for Vlasov equations
P.-E. Jabin · 2014
Later among the works it cites.
A multiscale meshfree method for macroscopic approximations of interacting particle systems
A. Klar and S. Tiwari · 2014
Later among the works it cites.
Convergence of a variational Lagrangian scheme for a nonlinear drift diffusion equation
H. Osberger and D. Matthes · 2014
Later among the works it cites.
Bakry–émery curvature-dimension condition and riemannian ricci curvature bounds
L. Ambrosio, N. Gigli, G. Savaré, et al · 2015
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Gradient Flows in Metric Spaces and in the Space of Probability Measures
L. Ambrosio, N. Gigli, and G. Savaré · 2008
Cited alongside, same era.
A gradient flow approach to an evolution problem arising in superconductivity
L. Ambrosio and S. Serfaty · 2008
Cited alongside, same era.
Convergence of the mass-transport steepest descent scheme for the sub-critical Patlak-Keller–Segel model
A. Blanchet, V. Calvez, and J. A. Carrillo · 2008
Cited alongside, same era.
Convergence of the mass-transport steepest descent scheme for the subcritical Patlak–Keller–Segel model
A. Blanchet, V. Calvez, and J. A. Carrillo · 2008
Cited alongside, same era.
Numerical simulation of diffusive and aggregation phenomena in nonlinear continuity equations by evolving diffeomorphisms
J. A. Carrillo and J. S. Moll · 2009
Cited alongside, same era.
Wasserstein distances for vortices approximation of Euler-type equations
M. Hauray · 2009
Cited alongside, same era.
Later among the works it cites.
Particle approximation of the one dimensional Keller–Segel equation, stability and rigidity of the blow-up
V. Calvez and T. O. Gallouët · 2015
Later among the works it cites.
Convergence of a linearly transformed particle method for aggregation equations
M. Campos-Pinto, J. A. Carrillo, F. Charles, and Y.-P. Choi · 2015
Later among the works it cites.
A finite-volume method for nonlinear nonlocal equations with a gradient flow structure
J. A. Carrillo, A. Chertock, and Y. Huang · 2015
Later among the works it cites.
Convergence of a fully discrete variational scheme for a thin-film equation
H. Osberger and D. Matthes · 2015
Later among the works it cites.
A convergent Lagrangian discretization for a nonlinear fourth order equation
H. Osberger and D. Matthes · 2015
Later among the works it cites.
Optimal Transport for Applied Mathematicians: Calculus of Variations, PDEs, and Modeling
F. Santambrogio · 2015
Later among the works it cites.
Existence of ground states of nonlocal-interaction energies
R. Simione, D. Slepčev, and I. Topaloglu · 2015
Later among the works it cites.
Local existence of weak solutions to kinetic models of granular media
M. Agueh · 2016
Later among the works it cites.
Discretization of functionals involving the Monge-Ampère operator
J.-D. Benamou, G. Carlier, Q. Mérigot, and E. Oudet · 2016
Later among the works it cites.
Convergence of a particle method for diffusive gradient flows in one dimension
J. A. Carrillo, F. S. Patacchini, P. Sternberg, and G. Wolansky · 2016
Later among the works it cites.
Numerical simulation of nonlinear continuity equations by evolving diffeomorphisms
J. A. Carrillo, H. Ranetbauer, and M.-T. Wolfram · 2016
Later among the works it cites.
A blob method for the aggregation equation
K. Craig and A. L. Bertozzi · 2016
Later among the works it cites.
Convergence of regularized nonlocal interaction energies
K. Craig and I. Topaloglu · 2016
Later among the works it cites.
Numerical study of a particle method for gradient flows
J. A. Carrillo, Y. Huang, F. S. Patacchini, and G. Wolansky · 2017
Closest in time.
Nonconvex gradient flow in the Wasserstein metric and applications to constrained nonlocal interactions
K. Craig · 2017
Closest in time.
Mean field limit for stochastic particle systems
P.-E. Jabin and Z. Wang · 2017
Closest in time.
A fully discrete variational scheme for solving nonlinear Fokker–Planck equations in multiple space dimensions
O. Junge, D. Matthes, and H. Osberger · 2017
Closest in time.
A random particle blob method for the Keller–Segel equation and convergence analysis
J.-G. Liu and R. Yang · 2017
Closest in time.
A Variational and Numerical Study of Aggregation-Diffusion Gradient Flows
F. S. Patacchini · 2017
Closest in time.
A discontinuous Galerkin method for nonlinear parabolic equations and gradient flow problems with interaction potentials, preprint
Z. Sun, J. A. Carrillo, and C.-W. Shu · 2017
Closest in time.