Analysis of pattern formation using numerical continuation

Vladimír Janovský

Displaying similar documents to “Analysis of pattern formation using numerical continuation”

Reaction-diffusion systems: Destabilizing effect of conditions given by inclusions

Jan Eisner (2000)

Mathematica Bohemica

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Sufficient conditions for destabilizing effects of certain unilateral boundary conditions and for the existence of bifurcation points for spatial patterns to reaction-diffusion systems of the activator-inhibitor type are proved. The conditions are related with the mollification method employed to overcome difficulties connected with empty interiors of appropriate convex cones.

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.

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

Ross G. Pinsky (2014)

Annales de l'I.H.P. Probabilités et statistiques

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We investigate the transience/recurrence of a non-Markovian, one-dimensional diffusion process which consists of a Brownian motion with a non-anticipating drift that has two phases – a transient to $+ \infty$ mode which is activated when the diffusion is sufficiently near its running maximum, and a recurrent mode which is activated otherwise. We also consider the speed of a diffusion with a two-phase drift, where the drift is equal to a certain non-negative constant when the diffusion is sufficiently...

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 $u_{t} - M (\int_{Ω} {| \nabla u |}^{2} d x) Δ u + {| u |}^{m (x) - 2} u_{t} = {| u |}^{r (x) - 2} u .$ We prove with suitable assumptions on the variable exponents $r (\cdot),$ $m (\cdot)$ 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.

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.

On the stability of the ALE space-time discontinuous Galerkin method for nonlinear convection-diffusion problems in time-dependent domains

Monika Balázsová, Miloslav Feistauer (2015)

Applications of Mathematics

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The paper is concerned with the analysis of the space-time discontinuous Galerkin method (STDGM) applied to the numerical solution of the nonstationary nonlinear convection-diffusion initial-boundary value problem in a time-dependent domain formulated with the aid of the arbitrary Lagrangian-Eulerian (ALE) method. In the formulation of the numerical scheme we use the nonsymmetric, symmetric and incomplete versions of the space discretization of diffusion terms and interior and boundary...

On estimation of diffusion coefficient based on spatio-temporal FRAP images: An inverse ill-posed problem

Kaňa, Radek, Matonoha, Ctirad, Papáček, Štěpán, Soukup, Jindřich

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We present the method for determination of phycobilisomes diffusivity (diffusion coefficient $D$ ) on thylakoid membrane from fluorescence recovery after photobleaching (FRAP) experiments. This was usually done by analytical models consisting mainly of a simple curve fitting procedure. However, analytical models need some unrealistic conditions to be supposed. Our method, based on finite difference approximation of the process governed by the Fickian diffusion equation and on the minimization...