Results 231 to 240 of about 38,842 (262)

Fractional-Order Evolutionary Integral Equations

Applied Mathematics and Computation, 1999
The author studies existence, uniqueness, and continuous dependence on data of solutions to fractional-order evolutionary integral equations of the form \[ D^\gamma u(t) = g(t) +\int_0^t f(t-s)Au(s) ds \] in a Banach space with the initial condition \(u(0)=0\) when \(\gamma \in (0,1]\) and \(u(0)=u_t(0) =0\) when \(\gamma \in (1,2]\).
Amer M A El Sayed
exaly   +2 more sources

Evolutionary blackbox control of Logistic equation

2009 European Control Conference (ECC), 2009
This research deals with optimization of the control of chaos by means of evolutionary algorithms. The main aim of this work is to show that evolutionary algorithms are capable of the optimization of chaos control and to show a new approach of solving this problem and constructing new cost functions operating in “blackbox mode” without previous exact ...
Roman Senkerik, Ivan Zelinka, Zuzana Oplatková   +2 more
openaire   +3 more sources

The Evolution of Evolutionary Equations

2002
“May you live in exciting times!” This traditional Chinese saying aptly describes the environment surrounding the basic developments in mathematics, physics, and chemistry over the past four centuries. From the founding of the European Academies of Sciences during the era of Peter the Great and Napoleon, to the founding of the National Science ...
George R. Sell, Yuncheng You
openaire   +1 more source

Attractors for Evolutionary Equations

2010
This chapter provides a survey of quantitative theory pertinent to long-time behavior of infinite-dimensional dissipative systems. The results are presented in a convenient form for applications to the material presented in subsequent chapters. For other possible approaches to the topic we refer to the monographs [17, 61, 134, 139, 172, 259, 273].
Igor Chueshov, Irena Lasiecka
openaire   +1 more source

GENERALIZATION OF THE PRICE EQUATION FOR EVOLUTIONARY CHANGE

Evolution, 2009
The Price equation is recognized as a general statistical description of evolutionary change with the potential to represent diverse processes. Here we present a new structurally symmetric equation for change that allows for arbitrary causal connectivity between ancestors and descendants, accounts for previously unaddressed processes (such as migration)
Benjamin, Kerr, Peter, Godfrey-Smith
openaire   +2 more sources

Moment equations in spatial evolutionary ecology

Journal of Theoretical Biology, 2016
How should we model evolution in spatially structured populations? Here, I review an evolutionary ecology approach based on the technique of spatial moment equations. I first provide a mathematical underpinning to the derivation of equations for the densities of various spatial configurations in network-based models.
openaire   +4 more sources

Homogenization of attractors of non--linear evolutionary equations

1999
The paper is devoted to the homogenization of nonlinear evolutionary equations in domains with ``traps''. The authors consider an initial boundary value problem for a semilinear parabolic equation of the form: \[ \frac{\partial u}{\partial t}- L_\varepsilon u+ f(u)= h, \quad t>0, \qquad u^\varepsilon (x,0)= u_0^\varepsilon (x), \] where \(L_\varepsilon\
Khruslov, E., Pankratov, L.
openaire   +3 more sources

Evolutionary Equations

2023
Heinrich Begehr, Robert P Gilbert
openaire   +1 more source

Basic Theory of Evolutionary Equations

2002
In the last chapter, we presented a theory describing solutions of a linear evolutionary equation ə t u + Au = 0, where \( {\partial _t}u = \frac{d}{{dt}}u \) on a Banach space W, in terms of C o-semigroups. As we have seen, this theory allows one to construct mild solutions of many linear partial differential equations with constant coefficients.
George R. Sell, Yuncheng You
openaire   +1 more source

Feedback Control for Nonlinear Evolutionary Equations With Applications

Nonlinear Analysis: Real World Applications, 2022
Biao Zeng
exaly