Prevalent Behavior of Strongly Order Preserving Semiflows
نویسندگان
چکیده
منابع مشابه
Prevalent Behavior of Strongly Order Preserving Semiflows
Classical results in the theory of monotone semiflows give sufficient conditions for the generic solution to converge toward an equilibrium or towards the set of equilibria (quasiconvergence). In this paper, we provide new formulations of these results in terms of the measure-theoretic notion of prevalence, developed in [1, 8]. For monotone reaction-diffusion systems with Neumann boundary condi...
متن کاملGeneric Quasi-Convergence for Essentially Strongly Order-Preserving Semiflows
By employing the limit set dichotomy for essentially strongly order-preserving semiflows and the assumption that limit sets have infima and suprema in the state space, we prove a generic quasi-convergence principle implying the existence of an open and dense set of stable quasi-convergent points. We also apply this generic quasi-convergence principle to a model for biochemical feedback in prote...
متن کاملGeneric Quasiconvergence for strongly order preserving semiflows: a new approach
The principal result of the theory of monotone semiflows says that for an open and dense set of initial data, the trajectory converges to the set of equilibria. We show that strong compactness assumptions on the semiflow, required for the proof, can be replaced by the assumption that limit sets have infimum and supremum in the space. This assumption is automatically satisfied in nice subsets of...
متن کاملLinear maps preserving or strongly preserving majorization on matrices
For $A,Bin M_{nm},$ we say that $A$ is left matrix majorized (resp. left matrix submajorized) by $B$ and write $Aprec_{ell}B$ (resp. $Aprec_{ell s}B$), if $A=RB$ for some $ntimes n$ row stochastic (resp. row substochastic) matrix $R.$ Moreover, we define the relation $sim_{ell s} $ on $M_{nm}$ as follows: $Asim_{ell s} B$ if $Aprec_{ell s} Bprec_{ell s} A.$ This paper characterizes all linear p...
متن کاملOn strongly Jordan zero-product preserving maps
In this paper, we give a characterization of strongly Jordan zero-product preserving maps on normed algebras as a generalization of Jordan zero-product preserving maps. In this direction, we give some illustrative examples to show that the notions of strongly zero-product preserving maps and strongly Jordan zero-product preserving maps are completely different. Also, we prove that the direct p...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Dynamics and Differential Equations
سال: 2007
ISSN: 1040-7294,1572-9222
DOI: 10.1007/s10884-007-9084-z