Displaying similar documents to “Transience, recurrence and speed of diffusions with a non-markovian two-phase “use it or lose it” drift”

Remarks on balanced norm error estimates for systems of reaction-diffusion equations

Hans-Goerg Roos (2018)

Applications of Mathematics

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Error estimates of finite element methods for reaction-diffusion problems are often realized in the related energy norm. In the singularly perturbed case, however, this norm is not adequate. A different scaling of the H 1 seminorm leads to a balanced norm which reflects the layer behavior correctly. We discuss the difficulties which arise for systems of reaction-diffusion problems.

Intertwining of the Wright-Fisher diffusion

Tobiáš Hudec (2017)

Kybernetika

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It is known that the time until a birth and death process reaches a certain level is distributed as a sum of independent exponential random variables. Diaconis, Miclo and Swart gave a probabilistic proof of this fact by coupling the birth and death process with a pure birth process such that the two processes reach the given level at the same time. Their coupling is of a special type called intertwining of Markov processes. We apply this technique to couple the Wright-Fisher diffusion...

A well-posedness result for a mass conserved Allen-Cahn equation with nonlinear diffusion

Kettani, Perla El, Hilhorst, Danielle, Lee, Kai

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In this paper, we prove the existence and uniqueness of the solution of the initial boundary value problem for a stochastic mass conserved Allen-Cahn equation with nonlinear diffusion together with a homogeneous Neumann boundary condition in an open bounded domain of ℝ n with a smooth boundary. We suppose that the additive noise is induced by a Q-Brownian motion.

Asymptotics for conservation laws involving Lévy diffusion generators

Piotr Biler, Grzegorz Karch, Wojbor A. Woyczyński (2001)

Studia Mathematica

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Let -ℒ be the generator of a Lévy semigroup on L¹(ℝⁿ) and f: ℝ → ℝⁿ be a nonlinearity. We study the large time asymptotic behavior of solutions of the nonlocal and nonlinear equations uₜ + ℒu + ∇·f(u) = 0, analyzing their L p -decay and two terms of their asymptotics. These equations appear as models of physical phenomena that involve anomalous diffusions such as Lévy flights.

Attractors for stochastic reaction-diffusion equation with additive homogeneous noise

Jakub Slavík (2021)

Czechoslovak Mathematical Journal

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We study the asymptotic behaviour of solutions of a reaction-diffusion equation in the whole space ℝ d driven by a spatially homogeneous Wiener process with finite spectral measure. The existence of a random attractor is established for initial data in suitable weighted L 2 -space in any dimension, which complements the result from P. W. Bates, K. Lu, and B. Wang (2013). Asymptotic compactness is obtained using elements of the method of short trajectories.

Geometry of non-holonomic diffusion

Simon Hochgerner, Tudor S. Ratiu (2015)

Journal of the European Mathematical Society

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We study stochastically perturbed non-holonomic systems from a geometric point of view. In this setting, it turns out that the probabilistic properties of the perturbed system are intimately linked to the geometry of the constraint distribution. For G -Chaplygin systems, this yields a stochastic criterion for the existence of a smooth preserved measure. As an application of our results we consider the motion planning problem for the noisy two-wheeled robot and the noisy snakeboard. ...

Analysis of pattern formation using numerical continuation

Vladimír Janovský (2022)

Applications of Mathematics

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The paper deals with the issue of self-organization in applied sciences. It is particularly related to the emergence of Turing patterns. The goal is to analyze the domain size driven instability: We introduce the parameter L , which scales the size of the domain. We investigate a particular reaction-diffusion model in 1-D for two species. We consider and analyze the steady-state solution. We want to compute the solution branches by numerical continuation. The model in question has certain...

Fast optical tracking of diffusion in time-dependent environment of brain extracellular space

Hrabě, Jan

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An improved version of the Integrative Optical Imaging (IOI) method for diffusion measurements in a geometrically complex environment of the brain extracellular space has been developed. We present a theory for this Fast Optical Tracking Of Diffusion (FOTOD) which incorporates a time-dependent effective diffusion coefficient in homogeneous anisotropic media with time-dependent nonspecific linear clearance. FOTOD can be used to measure rapid changes in extracellular diffusion permeability...

Global existence and stability of solution for a nonlinear Kirchhoff type reaction-diffusion equation with variable exponents

Aya Khaldi, Amar Ouaoua, Messaoud Maouni (2022)

Mathematica Bohemica

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We consider a class of Kirchhoff type reaction-diffusion equations with variable exponents and source terms u t - M ∫ Ω | ∇ u | 2 d x Δ u + | u | m ( x ) - 2 u t = | u | r ( x ) - 2 u . We prove with suitable assumptions on the variable exponents r ( · ) , m ( · ) the global existence of the solution and a stability result using potential and Nihari’s functionals with small positive initial energy, the stability being based on Komornik’s inequality.

Homogenization and Diffusion Asymptotics of the Linear Boltzmann Equation

Thierry Goudon, Antoine Mellet (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We investigate the diffusion limit for general conservative Boltzmann equations with oscillating coefficients. Oscillations have a frequency of the same order as the inverse of the mean free path, and the coefficients may depend on both slow and fast variables. Passing to the limit, we are led to an effective drift-diffusion equation. We also describe the diffusive behaviour when the equilibrium function has a non-vanishing flux.