• Title/Summary/Keyword: analytic semigroup theory

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BOUNDARY CONTROLLABILITY OF SEMILINEAR SYSTEMS IN BANACH SPACES

  • BALACHANDRAN, K.;ANANDHI, E.R.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.5 no.2
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    • pp.149-156
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    • 2001
  • Sufficient conditions for boundary controllability of semilinear systems in Banach spaces are established. The results are obtained by using the analytic semigroup theory and the Banach contraction principle. An example is provided to illustrate the theory.

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APPROXIMATIONS OF SOLUTIONS FOR A NONLOCAL FRACTIONAL INTEGRO-DIFFERENTIAL EQUATION WITH DEVIATED ARGUMENT

  • CHADHA, ALKA;PANDEY, DWIJENDRA N.
    • Journal of applied mathematics & informatics
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    • v.33 no.5_6
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    • pp.699-721
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    • 2015
  • This paper investigates the existence of mild solution for a fractional integro-differential equations with a deviating argument and nonlocal initial condition in an arbitrary separable Hilbert space H via technique of approximations. We obtain an associated integral equation and then consider a sequence of approximate integral equations obtained by the projection of considered associated nonlocal fractional integral equation onto finite dimensional space. The existence and uniqueness of solutions to each approximate integral equation is obtained by virtue of the analytic semigroup theory via Banach fixed point theorem. Next we demonstrate the convergence of the solutions of the approximate integral equations to the solution of the associated integral equation. We consider the Faedo-Galerkin approximation of the solution and demonstrate some convergenceresults. An example is also given to illustrate the abstract theory.

ASYMPTOTIC STABILITY OF STRONG SOLUTIONS FOR EVOLUTION EQUATIONS WITH NONLOCAL INITIAL CONDITIONS

  • Chen, Pengyu;Kong, Yibo;Li, Yongxiang
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.1
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    • pp.319-330
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    • 2018
  • This paper is concerned with the global asymptotic stability of strong solutions for a class of semilinear evolution equations with nonlocal initial conditions on infinite interval. The discussion is based on analytic semigroups theory and the gradually regularization method. The results obtained in this paper improve and extend some related conclusions on this topic.

PERTURBATION RESULTS FOR HYPERBOLIC EVOLUTION SYSTEMS IN HILBERT SPACES

  • Kang, Yong Han;Jeong, Jin-Mun
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.1
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    • pp.13-27
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    • 2014
  • The purpose of this paper is to derive a perturbation theory of evolution systems of the hyperbolic second order hyperbolic equations. We give an example of a partial functional equation as an application of the preceding result in case of the mixed problems for hyperbolic equations of second order with unbounded principal operators.

STEPANOV-LIKE PSEUDO ALMOST AUTOMORPHIC SOLUTIONS OF CLASS r IN 𝛼-NORM UNDER THE LIGHT OF MEASURE THEORY

  • DJENDODE MBAINADJI;ISSA ZABSONRE
    • Journal of Applied and Pure Mathematics
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    • v.5 no.3_4
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    • pp.129-164
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    • 2023
  • The aim of this work is to present some interesting results on weighted ergodic functions and prove the existence and uniqueness of Stepanov-like pseudo almost automorphic solutions using the spectral decomposition of the phase space developed by Adimy and co-authors. We also give the next challenge of this work.

ON THE GENERALIZED ORNSTEIN-UHLENBECK OPERATORS WITH REGULAR AND SINGULAR POTENTIALS IN WEIGHTED Lp-SPACES

  • Imen Metoui
    • Communications of the Korean Mathematical Society
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    • v.39 no.1
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    • pp.149-160
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    • 2024
  • In this paper, we give sufficient conditions for the generalized Ornstein-Uhlenbeck operators perturbed by regular potentials and inverse square potentials AΦ,G,V,c=∆-∇Φ·∇+G·∇-V+c|x|-2 with a suitable domain generates a quasi-contractive, positive and analytic C0-semigroup in Lp(ℝN , e-Φ(x)dx), 1 < p < ∞. The proofs are based on an Lp-weighted Hardy inequality and perturbation techniques. The results extend and improve the generation theorems established by Metoui [7] and Metoui-Mourou [8].

EXISTENCE OF SOLUTIONS OF QUASILINEAR INTEGRODIFFERENTIAL EVOLUTION EQUATIONS IN BANACH SPACES

  • Balachandran, Krishnan;Park, Dong-Gun
    • Bulletin of the Korean Mathematical Society
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    • v.46 no.4
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    • pp.691-700
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    • 2009
  • We prove the local existence of classical solutions of quasi-linear integrodifferential equations in Banach spaces. The results are obtained by using fractional powers of operators and the Schauder fixed-point theorem. An example is provided to illustrate the theory.