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
Global Existence and Boundedness of Solutions to a Model of Chemotaxis
A model of chemotaxis is analyzed that prevents blow-up of solutions. The model consists of a system of nonlinear partial differential equations for the spatial population density of a species and the spatial concentration of a chemoattractant in n-dimensional space. We prove the existence of solutions, which exist globally, and are L∞-bounded on finite time intervals. The hypotheses require nonlocal conditions on the species-induced production of the chemoattractant.
Global existence and convergence to steady states in a chemorepulsion system
In this paper we consider a model of chemorepulsion. We prove global existence and uniqueness of smooth classical solutions in space dimension n = 2. For n = 3,4 we prove the global existence of weak solutions. The convergence to steady states is shown in all cases.
Global existence for degenerate quadratic reaction-diffusion systems
Global existence for the discrete diffusive coagulation-fragmentation equations in L1.
Global existence of solutions for reaction-diffusion systems with a full matrix of diffusion coefficients and nonhomogeneous boundary conditions.
Global existence of solutions in invariant regions for reaction-diffusion systems with a balance law and a full matrix of diffusion coefficients.
Global existence of solutions to a chemotaxis system with volume filling effect
A system of quasilinear parabolic equations modelling chemotaxis and taking into account the volume filling effect is studied under no-flux boundary conditions. The resulting system is non-uniformly parabolic. A Lyapunov functional for the system is constructed. The proof of existence and uniqueness of regular global-in-time solutions is given in cases when either the Lyapunov functional is bounded from below or chemotactic forces are suitably weakened. In the first case solutions are uniformly...
Global existence, uniqueness, and continuous dependence for a reaction-diffusion equation with memory.
Global pointwise a priori bounds and large time behaviour for a nonlinear system describing the spread of infectious disease
This paper considers a reaction-diffusion system with biatic diffusion.Existence of a globally bounded solution is proved and its large timebehaviour is given.
Global solutions of a strongly coupled reaction-diffusion system with different diffusion coefficients.
Group actions on monotone skew-product semiflows with applications
We discuss a general framework of monotone skew-product semiflows under a connected group action. In a prior work, a compact connected group -action has been considered on a strongly monotone skew-product semiflow. Here we relax the strong monotonicity and compactness requirements, and establish a theory concerning symmetry or monotonicity properties of uniformly stable 1-cover minimal sets. We then apply this theory to show rotational symmetry of certain stable entire solutions for a class of...
Group Classification of Variable Coefficient Quasilinear Reaction-diffusion Equations