• Corpus ID: 235265916

A one-phase Stefan problem with non-linear diffusion from highly competing two-species particle systems

@inproceedings{Hayashi2021AOS,
  title={A one-phase Stefan problem with non-linear diffusion from highly competing two-species particle systems},
  author={Kohei Hayashi},
  year={2021}
}
Abstract. We consider an interacting particle system with two species under strong competition dynamics between the two species. Then, through the hydrodynamic limit procedure for the microscopic model, we derive a one-phase Stefan type free boundary problem with nonlinear diffusion, letting the competition rate divergent. Non-linearity of diffusion comes from a zero-range dynamics for one species while we impose the other species to weakly diffuse according to the Kawasaki dynamics for… 

References

SHOWING 1-10 OF 18 REFERENCES
Fast-reaction limit for Glauber-Kawasaki dynamics with two components
We consider the Kawasaki dynamics of two types of particles under a killing effect on a $d$-dimensional square lattice. Particles move with possibly different jump rates depending on their types. The
Spatial-segregation limit for exclusion processes with two components under unbalanced reaction
We consider exclusion processes with two types of particles which compete strongly with each other. In particular, we focus on the case where one species does not diffuse at all and killing rates of
Motion by Mean Curvature from Glauber–Kawasaki Dynamics
We study the hydrodynamic scaling limit for the Glauber-Kawasaki dynamics. It is known that, if the Kawasaki part is speeded up in a diffusive space-time scaling, one can derive the Allen-Cahn
Spatial segregation limit of a competition–diffusion system
We consider a competition–diffusion system and study its singular limit as the interspecific competition rate tend to infinity. We prove the convergence to a Stefan problem with zero latent heat.
Scaling Limits of Interacting Particle Systems
1. An Introductory Example: Independent Random Walks.- 2. Some Interacting Particle Systems.- 3. Weak Formulations of Local Equilibrium.- 4. Hydrodynamic Equation of Symmetric Simple Exclusion
On estimating the derivatives of symmetric diffusions in stationary random environment, with applications to ∇ϕ interface model
Abstract.We consider diffusions on ℝd or random walks on ℤd in a random environment which is stationary in space and in time and with symmetric and uniformly elliptic coefficients. We show existence
Vanishing, moving and immovable interfaces in fast reaction limits
Relative entropy and hydrodynamics of Ginzburg-Landau models
We prove the hydrodynamic limit of Ginzburg-Landau models by considering relative entropy and its rate of change with respect to local Gibbs states. This provides a new understanding of the role
Spectral gap for zero-range dynamics
We give a lower bound on the spectral gap for symmetric zero-range processes. Under some conditions on the rate function, we show that the gap shrinks as n -2 , independent of the density, for the
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