Results 11 to 20 of about 78 (78)
Datko criteria for uniform instability in Banach spaces [PDF]
, 2021 The main objective of this paper is to present some necessary and sufficient conditions of Datko type for the uniform exponential and uniform poly- nomial instability concepts for evolution operators in Banach spaces.
BORUGA (TOMA), Rovana, MEGAN, Mihail
core +2 more sources
Solvability of the abstract evolution equations in Ls-spaces with critical temporal weights
Open Mathematics, 2021 This paper deals with the abstract evolution equations in Ls{L}^{s}-spaces with critical temporal weights. First, embedding and interpolation properties of the critical Ls{L}^{s}-spaces with different exponents ss are investigated, then solvability of ...
Zhang Qinghua, Tan Zhizhong
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Estimates for evolutionary partial differential equations in classical function spaces
Forum of Mathematics, Sigma, 2023 We establish new local and global estimates for evolutionary partial differential equations in classical Banach and quasi-Banach spaces that appear most frequently in the theory of partial differential equations.
Alejandro J. Castro +3 more
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Open Mathematics, 2020 Given the abstract evolution equation y′(t)=Ay(t),t∈ℝ,y^{\prime} (t)=Ay(t),t\in {\mathbb{R}}, with a scalar type spectral operator A in a complex Banach space, we find conditions on A, formulated exclusively in terms of the location of its spectrum in ...
Markin Marat V.
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Admissible and weakly admissible observation operators for the right shift semigroup [PDF]
, 2002 In this note we show that two conjectures of George Weiss on admissible and weakly admissible observation operators fail to hold in general for the right shift semigroup in the case that the output space is infinite dimensional.AMS 2000 Mathematics ...
Partington, JR +5 more
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Open Mathematics, 2019 It is shown that, if all weak solutions of the evolution ...
Markin Marat V.
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On the uniform exponential stability of linear skew‐product semiflows
Journal of Function Spaces, Volume 4, Issue 2, Page 145-161, 2006., 2006 The problem of uniform exponential stability of linear skew‐product semiflows on locally compact metric space with Banach fibers, is discussed. It is established a connection between the uniform exponential stability of linear skewproduct semiflows and some admissibility‐type condition.
Ciprian Preda, Björn Birnir
wiley +1 more source
Method of semidiscretization in time for quasilinearintegrodifferential equations
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 9, Page 469-478, 2004., 2004 We consider a class of quasilinear integrodifferential equations in a reflexive Banach space. We apply the method of semidiscretization in time to establish the existence, uniqueness, and continuous dependence on the initial data of strong solutions.
D. Bahuguna, Reeta Shukla
wiley +1 more source
Existence, uniqueness, and regularity of solutions to semilinear retarded differential equations
International Journal of Stochastic Analysis, Volume 2004, Issue 3, Page 213-219, 2004., 2004 In the present work, we consider a semilinear retarded differential equation in a Banach space. We first establish the existence and uniqueness of a mild solution and then prove its regularity under different additional conditions. Finally, we consider some applications of the abstract results.
D. Bahuguna
wiley +1 more source
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