Results 71 to 80 of about 366 (188)

Weak almost periodic and optimal mild solutions of fractional evolution equations

Electronic Journal of Differential Equations, 2009
In this article, we prove the existence of optimal mild solutions for linear fractional evolution equations with an analytic semigroup in a Banach space.
Amar Debbouche, Mahmoud M. El-Borai
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The Algebraic Decay Behavior of Weak Solutions to the Magnetohydrodynamic Equations in Unbounded Domains

Mathematics
This paper investigates the long-term asymptotic behavior of solutions to the initial-boundary value problem for the three-dimensional incompressible viscous magnetohydrodynamic (MHD) equations in general unbounded domains. Addressing the difficulty that
Xuelin Chen, Mingjie Zhang
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An Equivalent Condition for Analytic C0-Semigroups

Journal of Mathematical Analysis and Applications, 1993
The paper studies the conditions on the infinitesimal generator of a \(C_ 0\)-semigroup under which it can be extended to an analytic semigroup. The condition is given by the following theorem. Theorem. Let \(T(t)\) be a \(C_ 0\)-semigroup with infinitesimal generator \(A\).
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Heat and Laplace type equations with complex spatial variables in weighted Fock spaces

Electronic Journal of Differential Equations, 2020
In a recent book co-authored by the authors of this article, we studied by semigroup theory methods several classical evolution equations, including the heat and Laplace equations, with real time variable and complex spatial variable, under the ...
Ciprian G. Gal, Sorin G. Gal
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On Liu's analyticity criterion for semigroups

Semigroup Forum, 1996
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Fractional Evolution Equation with Nonlocal Multi-Point Condition: Application to Fractional Ginzburg–Landau Equation

Axioms
This paper is devoted to studying the existence and uniqueness of mild solutions for semilinear fractional evolution equations with the Hilfer–Katugampola fractional derivative and under the nonlocal multi-point condition.
Ahmed Salem, Rania Al-Maalwi
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Integrodifferential equations with analytic semigroups

International Journal of Stochastic Analysis, 2001
In this paper we study a class of integrodifferential equations considered in an arbitrary Banach space. Using the theory of analytic semigroups we establish the existence, uniqueness, regularity and continuation of solutions to these integrodifferential equations.
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Approximations of solutions to nonlinear Sobolev type evolution equations

Electronic Journal of Differential Equations, 2003
In the present work we study the approximations of solutions to a class of nonlinear Sobolev type evolution equations in a Hilbert space. These equations arise in the analysis of the partial neutral functional differential equations with unbounded delay.
Dhirendra Bahuguna, Reeta Shukla
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On the uniqueness of mild solutions and an averaging principle results for partial functional differential equations with infinite delay using the α-norm

Electronic Journal of Qualitative Theory of Differential Equations
In this paper, we study a class of partial functional differential equations with infinite delay within an abstract phase space framework. By employing the $\alpha$-norm, we establish the existence and uniqueness of mild solutions under a more general ...
Zakaria Elhafiane, Khalil Ezzinbi
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Solutions to quasi-linear differential equations with iterated deviating arguments

Electronic Journal of Differential Equations, 2014
We establish sufficient conditions for the existence and uniqueness of solutions to quasi-linear differential equations with iterated deviating arguments, complex Banach space.
Rajib Haloi
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