Space dimension can prevent the blow-up of solutions for parabolic problems.
Spatial Dynamics of Contact-Activated Fibrin Clot Formation in vitro and in silico in Haemophilia B: Effects of Severity and Ahemphil B Treatment
Spatial dynamics of fibrin clot formation in non-stirred system activated by glass surface was studied as a function of FIX activity. Haemophilia B plasma was obtained from untreated patients with different levels of FIX deficiency and from severe haemophilia B patient treated with FIX concentrate (Ahemphil B) during its clearance with half-life t1/2=12 hours. As reported previously (Ataullakhanov et al. Biochim Biophys Acta 1998; 1425: 453-468), clot growth in space showed two distinct phases:...
Spatial patterns for reaction-diffusion systems with conditions described by inclusions
We consider a reaction-diffusion system of the activator-inhibitor type with boundary conditions given by inclusions. We show that there exists a bifurcation point at which stationary but spatially nonconstant solutions (spatial patterns) bifurcate from the branch of trivial solutions. This bifurcation point lies in the domain of stability of the trivial solution to the same system with Dirichlet and Neumann boundary conditions, where a bifurcation of this classical problem is excluded.
Spatial tumor-immune modeling.
Spatially-dependent and nonlinear fluid transport: coupling framework
We introduce a solver method for spatially dependent and nonlinear fluid transport. The motivation is from transport processes in porous media (e.g., waste disposal and chemical deposition processes). We analyze the coupled transport-reaction equation with mobile and immobile areas. The main idea is to apply transformation methods to spatial and nonlinear terms to obtain linear or nonlinear ordinary differential equations. Such differential equations can be simply solved with Laplace transformation...
Speed-up of reaction-diffusion fronts by a line of fast diffusion
In these notes, we discuss a new model, proposed by H. Berestycki, J.-M. Roquejoffre and L. Rossi, to describe biological invasions in the plane when a strong diffusion takes place on a line. This model seems relevant to account for the effects of roads on the spreading of invasive species. In what follows, the diffusion on the line will either be modelled by the Laplacian operator, or the fractional Laplacian of order less than 1. Of interest to us is the asymptotic speed of spreading in the direction...
Spread Pattern Formation of H5N1-Avian Influenza and its Implications for Control Strategies
Mechanisms contributing to the spread of avian influenza seem to be well identified, but how their interplay led to the current worldwide spread pattern of H5N1 influenza is still unknown due to the lack of effective global surveillance and relevant data. Here we develop some deterministic models based on the transmission cycle and modes of H5N1 and focusing on the interaction among poultry, wild birds and environment. Some of the model parameters are obtained from existing literatures, and others...
Stability analysis of a model of atherogenesis: an energy estimate approach. II.
Stability analysis of a model of atherogenesis: an energy estimate approach.
Stability analysis of a ratio-dependent predator-prey system with diffusion and stage structure.
Stability and bifurcation problems for reaction-diffusion systems with unilateral conditions
Stability criteria for a class of discrete reaction-diffusion equations.
Stability of fixed points for order-preserving discrete-time dynamical systems.
Stability of radially symmetric travelling waves in reaction–diffusion equations
Stability of stochastic reaction-diffusion recurrent neural networks with unbounded distributed delays.
Stability of traveling waves and a relation between the Evans function and the SLEP equation.
Stability of travelling waves in a model for conical flames in two space dimensions
Stability properties of non-negative solutions of semilinear symmetric cooperative systems.
Stabilization for a periodic predator-prey system.
Stabilization of solutions of a reaction-diffusion equation