Nonlinear asymptotic stability of the equilibrium state for the MEP model of charge transport in semiconductors

2006 ◽  
Vol 65 (11) ◽  
pp. 2169-2191 ◽  
Author(s):  
A.M. Blokhin ◽  
R.S. Bushmanov ◽  
V. Romano
Keyword(s):  
Asymptotic Stability ◽  
Equilibrium State ◽  
Charge Transport

ASYMPTOTIC STABILITY OF EQUILIBRIUM STATES FOR MULTICOMPONENT REACTIVE FLOWS

1998 ◽  
Vol 08 (02) ◽  
pp. 251-297 ◽  
Author(s):  
VINCENT GIOVANGIGLI ◽  
MARC MASSOT
Keyword(s):  
Asymptotic Stability ◽  
Normal Form ◽  
Equilibrium State ◽  
Source Term ◽  
Null Space ◽  
Entropy Function ◽  
Reactive Flows ◽  
Constant Equilibrium ◽  
Systems Of Conservation Laws ◽  
Symmetric Systems

We consider the equations governing multicomponent reactive flows derived from the kinetic theory of dilute polyatomic reactive gas mixtures. Using an entropy function, we derive a symmetric conservative form of the system. In the framework of Kawashima and Shizuta's theory, we recast the resulting system into a normal form, that is, in the form of a symmetric hyperbolic–parabolic composite system. We also characterize all normal forms for symmetric systems of conservation laws such that the null space associated with dissipation matrices is invariant. We then investigate an abstract second-order quasilinear system with a source term, around a constant equilibrium state. Assuming the existence of a generalized entropy function, the invariance of the null space naturally associated with dissipation matrices, stability conditions for the source term, and a dissipative structure for the linearized equations, we establish global existence and asymptotic stability around the constant equilibrium state in all space dimensions and we obtain decay estimates. These results are then applied to multicomponent reactive flows using a normal form and the properties of Maxwellian chemical source terms.

scholarly journals Stability of Sets Criteria for Impulsive Cohen-Grossberg Delayed Neural Networks with Reaction-Diffusion Terms

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 27 ◽  
Author(s):  
Gani Stamov ◽  
Stefania Tomasiello ◽  
Ivanka Stamova ◽  
Cvetelina Spirova
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Asymptotic Stability ◽  
Equilibrium State ◽  
Global Exponential Stability ◽  
Lyapunov Method ◽  
Reaction Diffusion ◽  
Delayed Neural Networks ◽  
The Stability ◽  
Impulsive Reaction

The paper proposes an extension of stability analysis methods for a class of impulsive reaction-diffusion Cohen-Grossberg delayed neural networks by addressing a challenge namely stability of sets. Such extended concept is of considerable interest to numerous systems capable of approaching not only one equilibrium state. Results on uniform global asymptotic stability and uniform global exponential stability with respect to sets for the model under consideration are established. The main tools are expansions of the Lyapunov method and the comparison principle. In addition, the obtained results for the uncertain case contributed to the development of the stability theory of uncertain reaction-diffusion Cohen-Grossberg delayed neural networks and their applications. Moreover, examples are given to demonstrate the feasibility of our results.

A Hitherto Undescribed Naturally Occurring Plasma Antagonist of Activated Factor X Inhibitor (Antithrombin III)

1979 ◽  
Author(s):  
E. T. Yin ◽  
W. J. Salsgiver ◽  
O. Tangen
Keyword(s):  
Equilibrium State ◽  
Human Plasma ◽  
Antithrombin Iii ◽  
Circumstantial Evidence ◽  
Incubation Mixture ◽  
Factor X ◽  
Normal Human Plasma ◽  
Plasma Component ◽  
Naturally Occurring ◽  
Normal Human

Circumstantial evidence suggested that normal human plasma contained a substance regulating the neutralization of F.Xa by F.Xa inhibitor(XaI), (Yin et.al.,Adv.Exper. Med. & Biol., 52 : 239, 1975, Plenum Press, N.Y.).This plasma component has now been isolated and partially purified in our laboratory, and tentatively designated as “Anti-XaI”.In experiments employing purified components, when Anti-XaI was incubated at 37°C with F.Xa, Xal and heparin for two minutes at pH7.5, the amount of F.Xa inhibited was inversely proportional to the Anti-XaI concentration. But, when the F.Xa was replaced by thrombin in the incubation mixture, the neutralization of thrombin clotting activity was undisturbed.Anti-XaI was found to be neither PF3 nor PF4.These and other data strongly suggest that the “Antithrombin III pathway” is more complex than currently believed to be. In circulating blood an equilibrium state must exist between Anti-XaI and XaI.Under certain conditions when the Anti-XaI activity is predominant the rate of F.Xa neutralization bv XaI then becomes slower than the activation of prothrombin to thrombin by F.Xa.

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