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Asymptotic behavior of the numerical solutions of time-delayed reaction diffusion equations with non-monotone reaction term

Yuan-Ming Wang (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

This paper is concerned with the asymptotic behavior of the finite difference solutions of a class of nonlinear reaction diffusion equations with time delay. By introducing a pair of coupled upper and lower solutions, an existence result of the solution is given and an attractor of the solution is obtained without monotonicity assumptions on the nonlinear reaction function. This attractor is a sector between two coupled quasi-solutions of the corresponding “steady-state” problem, which are obtained...

Asymptotic behavior of the numerical solutions of time-delayed reaction diffusion equations with non-monotone reaction term

Yuan-Ming Wang (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper is concerned with the asymptotic behavior of the finite difference solutions of a class of nonlinear reaction diffusion equations with time delay. By introducing a pair of coupled upper and lower solutions, an existence result of the solution is given and an attractor of the solution is obtained without monotonicity assumptions on the nonlinear reaction function. This attractor is a sector between two coupled quasi-solutions of the corresponding “steady-state" problem, which are...

Asymptotically self-similar solutions for the parabolic system modelling chemotaxis

Yūki Naito (2006)

Banach Center Publications

We consider a nonlinear parabolic system modelling chemotaxis u t = ∇ · ( ∇ u - u ∇ v ) , v t = Δ v + u in ℝ², t > 0. We first prove the existence of time-global solutions, including self-similar solutions, for small initial data, and then show the asymptotically self-similar behavior for a class of general solutions.

Atherosclerosis Initiation Modeled as an Inflammatory Process

N. El Khatib, S. Génieys, V. Volpert (2010)

Mathematical Modelling of Natural Phenomena

In this work we study the inflammatory process resulting in the development of atherosclerosis. We develop a one- and two-dimensional models based on reaction-diffusion systems to describe the set up of a chronic inflammatory response in the intima of an artery vessel wall. The concentration of the oxidized low density lipoproteins (ox-LDL) in the intima is the critical parameter of the model. Low ox-LDL concentrations do not lead to a chronic inflammatory reaction. Intermediate ox-LDL concentrations...

Attractors for stochastic reaction-diffusion equation with additive homogeneous noise

Jakub Slavík (2021)

Czechoslovak Mathematical Journal

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.

Behaviour of global solutions for a system of reaction-diffusion equations from combustion theory

Salah Badraoui (1999)

Applicationes Mathematicae

We are concerned with the boundedness and large time behaviour of the solution for a system of reaction-diffusion equations modelling complex consecutive reactions on a bounded domain under homogeneous Neumann boundary conditions. Using the techniques of E. Conway, D. Hoff and J. Smoller [3] we also show that the bounded solution converges to a constant function as t → ∞. Finally, we investigate the rate of this convergence.

Currently displaying 61 – 80 of 445