Results 21 to 30 of about 938 (62)

Asymptotic almost periodicity of C‐semigroups

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 2, Page 65-73, 2003., 2003
Let {T(t)}t≥0 be a C‐semigroup on a Banach space X with generator A. We will investigate the asymptotic almost periodicity of {T(t)} via the Hille‐Yosida space of its generator.
Linghong Xie, Miao Li, Falun Huang
wiley   +1 more source

On quasi-contractivity of C 0-semigroups on Banach spaces [PDF]

, 2004
A basic result in semigroup theory states that every C-0-semigroup is quasi-contractive with respect to some appropriately chosen equivalent norm. This paper contains a counterpart of this well-known fact.
Matolcsi, Máté
core   +1 more source

The Kneser property for abstract retarded functional differential equations with infinite delay

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 26, Page 1645-1661, 2003., 2003
We establish existence of mild solutions for a class of semilinear first‐order abstract retarded functional differential equations (ARFDEs) with infinite delay and we prove that the set consisting of mild solutions for this problem is connected in the space of continuous functions.
Hernán R. Henríquez
wiley   +1 more source

Linear neutral partial differential equations: a semigroup approach

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 23, Page 1433-1445, 2003., 2003
We study linear neutral PDEs of the form (∂/∂t)Fut = BFut + Φut, t ≥ 0; u0(t) = φ(t), t ≤ 0, where the function u(⋅) takes values in a Banach space X. Under appropriate conditions on the difference operator F and the delay operator Φ, we construct a C0‐semigroup on C0(ℝ−, X) yielding the solutions of the equation.
Rainer Nagel, Nguyen Thieu Huy
wiley   +1 more source

Topological structure of solution sets of differential inclusions: the constrained case

Abstract and Applied Analysis, Volume 2003, Issue 6, Page 325-351, 2003., 2003
We survey and announce some current results on the existence, the viability, and the topological structure of the viable solutions of differential equations and inclusion in Banach spaces under set constraints. Some new results concerning semilinear differential inclusions with state variables constrained to the so‐called regular and strictly regular ...
Wojciech Kryszewski
wiley   +1 more source

On the mild solutions of higher‐order differential equations in Banach spaces

Abstract and Applied Analysis, Volume 2003, Issue 15, Page 865-880, 2003., 2003
For the higher‐order abstract differential equation u(n)(t) = Au(t) + f(t), t ∈ ℝ, we give a new definition of mild solutions. We then characterize the regular admissibility of a translation‐invariant subspace ℳ of BUC(ℝ, E) with respect to the above‐mentioned equation in terms of solvability of the operator equation AX − X𝒟n = C.
Nguyen Thanh Lan
wiley   +1 more source

A spectral mapping theorem for semigroups solving PDEs with nonautonomous past

Abstract and Applied Analysis, Volume 2003, Issue 16, Page 933-951, 2003., 2003
We prove a spectral mapping theorem for semigroups solving partial differential equations with nonautonomous past. This theorem is then used to give spectral conditions for the stability of the solutions of the equations.
Genni Fragnelli
wiley   +1 more source

Applications of Stochastic Semigroups to Queueing Models

Annales Mathematicae Silesianae, 2019
Non-markovian queueing systems can be extended to piecewise-deterministic Markov processes by appending supplementary variables to the system. Then their analysis leads to an infinite system of partial differential equations with an infinite number of ...
Gwiżdż Piotr
doaj   +1 more source

Large diffusivity finite‐dimensional asymptotic behaviour of a semilinear wave equation

Journal of Applied Mathematics, Volume 2003, Issue 8, Page 409-427, 2003., 2003
We study the effects of large diffusivity in all parts of the domain in a linearly damped wave equation subject to standard zero Robin‐type boundary conditions. In the linear case, we show in a given sense that the asymptotic behaviour of solutions verifies a second‐order ordinary differential equation.
Robert Willie
wiley   +1 more source

A note on the spectral operators of scalar type and semigroups of bounded linear operators

International Journal of Mathematics and Mathematical Sciences, Volume 32, Issue 10, Page 635-640, 2002., 2002
It is shown that, for the spectral operators of scalar type, the well‐known characterizations of the generation of C0‐ and analytic semigroups of bounded linear operators can be reformulated exclusively in terms of the spectrum of such operators, the conditions on the resolvent of the generator being automatically met and the corresponding semigroup ...
Marat V. Markin
wiley   +1 more source