Results 21 to 30 of about 378 (71)

The discrete fragmentation equations : semigroups, compactness and asynchronous exponential growth [PDF]

, 2012
In this paper we present a class of fragmentation semigroups which are compact in a scale of spaces defined in terms of finite higher moments. We use this compactness result to analyse the long time behaviour of such semigroups and, in particular, to ...
A. C. McBride, A. L. Smith, F. P. da Costa, J. Banasiak, J. Banasiak, J. Banasiak, J. Banasiak, J. Carr, J. M. Ball, Jacek Banasiak, K. Pichór, K.-J. Engel, K.-J. Engel, P. Glendinning, P. Laurençot, Ph. Clément, R. Rudnicki, T. Kato, W. Arendt, Wilson Lamb   +19 more
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ERRATUM TO: ``CONDITIONAL SOLVABILITY OF THE BOUNDARY VALUE PROBLEM OF A SELF-ADJOINT OPERATOR-DIFFERENTIAL EQUATIONS IN A SOBOLEV-TYPE SPACE'',In: \emph{Int. J. Appl. Math.}, {\bf 32}, No 3 (2019), 469-478; by M.A. Labeeb, A.B.I. Ahmed, L. Rashed; doi: 10.12732/ijam.v32i3.8

, 2019
This is a critical note sent to Editor-in-Chief of the journal. The comments are based on a personal view of the author, on whose works the discussed paper is based in parts.
A. R. Aliev
semanticscholar   +1 more source

On almost automorphic solutions of linear operational‐differential equations

International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 22, Page 1179-1182, 2004., 2004
We prove almost periodicity and almost automorphy of bounded solutions of linear differential equations x′(t) = Ax(t) + f(t) for some class of linear operators acting in a Banach space.
Gaston M. N′Guérékata
wiley   +1 more source

On a higher‐order evolution equation with a Stepanov‐bounded solution

International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 72, Page 3959-3964, 2004., 2004
We study strong solutions u : ℝ → X, a Banach space X, of the nth‐order evolution equation u(n) − Au(n−1) = f, an infinitesimal generator of a strongly continuous group A : D(A)⊆X → X, and a given forcing term f : ℝ → X. It is shown that if X is reflexive, u and u(n−1) are Stepanov‐bounded, and f is Stepanov almost periodic, then u and all derivatives ...
Aribindi Satyanarayan Rao
wiley   +1 more source

A class of linear dynamical equations for a Banach space on time scales

Advances in Differential Equations, 2013
In this paper we consider the existence and uniqueness of global solutions to linear dynamical equations for a Banach space on time scales from a new point of view.
Youling Feng
semanticscholar   +2 more sources

On scalar type spectral operators, infinite differentiable and Gevrey ultradifferentiable C0‐semigroups

International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 45, Page 2401-2422, 2004., 2004
Necessary and sufficient conditions for a scalar type spectral operator in a Banach space to be a generator of an infinite differentiable or a Gevrey ultradifferentiable C0‐semigroup are found, the latter formulated exclusively in terms of the operator′s spectrum.
Marat V. Markin
wiley   +1 more source

Fragmentation arising from a distributional initial condition [PDF]

, 2010
A standard model for pure fragmentation is subjected to an initial condition of Dirac-delta type. Results for a corresponding abstract Cauchy problem are derived via the theory of equicontinuous semigroups of operators on locally convex spaces.
Aizenman, Banasiak, Belleni-Morante, Belleni-Morante, Erdélyi, Gel'fand, Kōmura, Lamb, Lebedev, Lisi, McBride, McBride, McGrady, Zemanian, Ziff, Ziff   +15 more
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The fundamental solutions for fractional evolution equations of parabolic type

International Journal of Stochastic Analysis, Volume 2004, Issue 3, Page 197-211, 2004., 2004
The fundamental solutions for linear fractional evolution equations are obtained. The coefficients of these equations are a family of linear closed operators in the Banach space. Also, the continuous dependence of solutions on the initial conditions is studied. A mixed problem of general parabolic partial differential equations with fractional order is
Mahmoud M. El-Borai
wiley   +1 more source

Abstract fractional integro-differential equations involving nonlocal initial conditions in α-norm

, 2011
In the present paper, we deal with the Cauchy problems of abstract fractional integro-differential equations involving nonlocal initial conditions in α-norm, where the operator A in the linear part is the generator of a compact analytic semigroup.
Rongnian Wang, Jun Liu, De-Han Chen
semanticscholar   +1 more source

Hyperbolic differential‐operator equations on a whole axis

Abstract and Applied Analysis, Volume 2004, Issue 2, Page 99-113, 2004., 2004
We give an abstract interpretation of initial boundary value problems for hyperbolic equations such that a part of initial boundary value conditions contains also a differentiation on the time t of the same order as equations. The case of stable solutions of abstract hyperbolic equations is treated.
Yakov Yakubov
wiley   +1 more source