Extinction and non-extinction of solutions for a nonlocal reaction-diffusion problem.
Extremal equilibria for parabolic non-linear reaction-diffusion equations
Fast and heteroclinic solutions for a second order ODE.
Finite dimensional dynamics for Kolmogorov-Petrovsky-Piskunov equation.
Finite fractal dimension of pullback attractors and application to non-autonomous reaction diffusion equations.
Finite-dimensional pullback attractors for parabolic equations with Hardy type potentials
Using the asymptotic a priori estimate method, we prove the existence of a pullback -attractor for a reaction-diffusion equation with an inverse-square potential in a bounded domain of (N ≥ 3), with the nonlinearity of polynomial type and a suitable exponential growth of the external force. Then under some additional conditions, we show that the pullback -attractor has a finite fractal dimension and is upper semicontinuous with respect to the parameter in the potential.
Flame Propagation through Large-Scale Vortical Flows: Effect of Equivalence Ratio
The present work is a continuation of previous studies of premixed gas flames spreading through a space-periodic array of large-scale vorticities, and is motivated by the experimentally known phenomenon of flame extinction by turbulence. The prior work dealt with the strongly non-stoichiometric limit where the reaction rate is controlled by a single (deficient) reactant. In the present study the discussion is extended over a physically more realistic formulation based on a bimolecular reaction...
Flow invariance for perturbed nonlinear evolution equations.
Forced anisotropic mean curvature flow of graphs in relative geometry
The paper is concerned with the graph formulation of forced anisotropic mean curvature flow in the context of the heteroepitaxial growth of quantum dots. The problem is generalized by including anisotropy by means of Finsler metrics. A semi-discrete numerical scheme based on the method of lines is presented. Computational results with various anisotropy settings are shown and discussed.
Forced periodic oscillations in the climate system via an energy balance model
Front propagation for nonlinear diffusion equations on the hyperbolic space
We study the Cauchy problem in the hyperbolic space for the semilinear heat equation with forcing term, which is either of KPP type or of Allen-Cahn type. Propagation and extinction of solutions, asymptotical speed of propagation and asymptotical symmetry of solutions are addressed. With respect to the corresponding problem in the Euclidean space new phenomena arise, which depend on the properties of the diffusion process in . We also investigate a family of travelling wave solutions, named...
Front propagation for reaction-diffusion equations of bistable type
Full discretization of some reaction diffusion equation with blow up
This paper aims at the development of numerical schemes for nonlinear reaction diffusion problems with a convection that blows up in a finite time. A full discretization of this problem that preserves the blow - up property is presented as well as a numerical simulation. Efficiency of the method is derived via a numerical comparison with a classical scheme based on the Runge Kutta scheme.
Gas-solid reaction with porosity change.
Genetic Exponentially Fitted Method for Solving Multi-dimensional Drift-diffusion Equations
A general approach was proposed in this article to develop high-order exponentially fitted basis functions for finite element approximations of multi-dimensional drift-diffusion equations for modeling biomolecular electrodiffusion processes. Such methods are highly desirable for achieving numerical stability and efficiency. We found that by utilizing the one-to-one correspondence between the continuous piecewise polynomial space of degree k + 1 and the divergencefree vector space of degree k, one...
Global Asymptotic Stability of Equilibria in Models for Virus Dynamics
In this paper several models in virus dynamics with and without immune response are discussed concerning asymptotic behaviour. The case of immobile cells but diffusing viruses and T-cells is included. It is shown that, depending on the value of the basic reproductive number R0 of the virus, the corresponding equilibrium is globally asymptotically stable. If R0 < 1 then the virus-free equilibrium has this property, and in case R0 > 1 there is a unique disease equilibrium which takes over this...
Global behaviour of solutions to some nonlinear diffusion equations
Global dynamics of a reaction-diffusion system.
Global existence and blow up of solutions for a completely coupled Fujita type system of reaction-diffusion equations
We examine the parabolic system of three equations - Δu = , - Δv = , - Δw = , x ∈ , t > 0 with p, q, r positive numbers, N ≥ 1, and nonnegative, bounded continuous initial values. We obtain global existence and blow up unconditionally (that is, for any initial data). We prove that if pqr ≤ 1 then any solution is global; when pqr > 1 and max(α,β,γ) ≥ N/2 (α, β, γ are defined in terms of p, q, r) then every nontrivial solution exhibits a finite blow up time.
Global existence and blow-up for a completely coupled Fujita type system
The Fujita type global existence and blow-up theorems are proved for a reaction-diffusion system of m equations (m>1) in the form