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Behaviour near extinction for the Fast Diffusion Equation on bounded domains
Nonlinear evolution singular parabolic fast di usion Harnack asymptotics
2011/1/18
We consider the Fast Di usion Equation ut = um posed in a bounded smooth domain
Rd with homogeneous Dirichlet conditions; the exponent range is ms = (d 2)+=(d + 2) < m < 1.It is known...
Superdiffusive bounds on self-repellent Brownian polymers and diffusion in the curl of the Gaussian free field in d=2
self-repelling random motion diffusion in random environment super-diffusivity
2011/2/28
We consider two models of random diffusion in random environment in two dimensions. The first example is the self-repelling Brownian polymer, this describes a diffusion pushed by the negative gradient...
Application of Sumudu transform in reaction-diffusion systems and nonlinear waves
Fractional diffusion equation Generalized Mittag-Liffler Function
2010/9/20
In this paper we investigate the solution of a nonlinear reactiondiffusion equation connected with nonlinear waves by the application of Sumudu transform. The results presented here are in compact and...
Comparison of third order L_0-stable numerical schemes for the two–Dimensional homogeneous diffusion problem subject to specification of mass
Lo − stable Parabolic Problems
2010/9/21
This paper presents a numerical comparison of third order Lo − stable numerical schemes for the two-dimensional parabolic partial differential equations subject to nonlocal boundary conditions. ...
On the output stabilizability of the diffusion equation
Infinite dimensional systems controllability
2010/9/25
This note is devoted to study the output stabilizability of a simplified and a one-dimensional diffusion equation. Necessary and sufficient conditions for the system to be output stabilizable will be ...
A modified backward Euler scheme for the diffusion equation subject to purely integral conditions
Diffusion equation Modified backward Euler method
2010/9/25
In this paper, a modified backward Euler scheme is developped for obtaining approximate solution to the initial-boundary value problem for one-dimensional diffusion equation with purely integral condi...
Asymptotic and bifurcation analysis of wave-pinning in a reaction-diffusion model for cell polarization
Asymptotic bifurcation analysis wave-pinning reaction-diffusion model
2011/1/5
We describe and analyze a bistable reaction-diffusion (RD) model for two interconverting chemical species that exhibits a phenomenon of wave-pinning: a wave of activation of one of the species is init...
Convergence of the Dirichlet solutions of the very fast diffusion equation
very fast diffusion equation Dirichlet problem
2011/2/21
For any −1 < m < 0, μ > 0, 0 ≤ u0 ∈ L∞(R) such that u0(x) ≤ (μ0|m||x|) 1 m for any |x| ≥ R0 and some constants R0 > 1 and 0 < μ0 ≤ μ, and f, g ∈C([0,∞)) such that f(t), g(t) ≥ μ0 on [0,∞) we pro...
On the differentiability of the solution to an equation with drift and fractional diffusion
differentiability solution equation drift fractional diffusion
2011/1/20
We consider an equation with drift and either critical or supercritical fractional diffusion.
Under a regularity assumption for the vector field that is marginally stronger than what is required for ...
Transport barrier for the radial diffusion due to the ExB drift motion of guiding centers in cylindrical confinement geometry
Transport barrier for the radial diffusion ExB drift motion cylindrical confinement geometry
2010/12/28
We consider the radial transport of test particles due to the E×B drift motion in the guiding center approximation. In a configuration where the magnetic field is constant and uniform in linear device...
Excluded-volume effects in the diffusion of hard spheres
Excluded-volume effects diffusion of hard spheres
2011/1/21
Excluded-volume effects can play an important role in determining transport properties in diffusion of particles through crowded environments.
Extinction profile of the logarithmic diffusion equation
logarithmic diffusion equation extinction profile asymptotic behaviour
2011/1/19
Let u be the solution of ut = log u in RN × (0, T ), N ≥ 3, with initial value u0 satisfying Bk1 (x, 0) ≤ u0 ≤ Bk2(x, 0) for some constants k1 > k2 > 0 where Bk(x, t) = 2(N − 2)(T −t)N/(N...
Application of Operator Splitting to Solve Reaction Diffusion Equations
Solve Reaction Diffusion Equations math
2010/11/24
Approximate solutions of the Fisher equation obtained by different splitting methods are investigated. The error of this nonlinear problem is analyzed. The order of different splitting methods coupled...
Degenerate diffusion with a drift potential: a viscosity solutions approach, joint work with I. C. Kim, truncated version
drift potential viscosity solutions approach
2010/11/23
This is a truncated version of the paper "Degenerate diffusion with a drift potential: a viscosity solutions approach", co-authored with I. C. Kim. The purpose of this version is to withdraw the claim...
Asymptotic Limit of a Singularly Perturbed Stationary Diffusion Equation: The Case of a Limit Cycle
Diffusion Equation Limit Cycle
2010/11/23
A limit cycle for a nonlinear ordinary differential equation has a sustained, stationary oscillation in time; Any non-trivial stationary stochastic process also exhibits stationary oscillations in tim...