Initial and boundary value problems for functional integro-differential equations.
Initial value problems for integro-differential equations of Volterra type in Banach spaces.
Integral inequalities of Gronwall type for piecewise continuous functions.
Integral Perturbations of Nonlinear Systems of Differential Equations
Integral repesentations and its applications in Clifford analysis.
Integrated semigroups and integrodifferential equations.
Integrodifferential equations with analytic semigroups.
Integro-differential equations with time-varying delay
Integro-differential equations with time-varying delay can provide us with realistic models of many real world phenomena. Delayed Lotka-Volterra predator-prey systems arise in ecology. We investigate the numerical solution of a system of two integro-differential equations with time-varying delay and the given initial function. We will present an approach based on -step methods using quadrature formulas.
Integrodifferential inequality for stability of singularly perturbed impulsive delay integrodifferential equations.
Linear abstract integro-differential equations of hyperbolic type in Hilbert spaces
Linear boundary value type problems for functional-differential equations and their adjoints
Linear integro-differential equations in Banach spaces
Long-time dynamics of an integro-differential equation describing the evolution of a spherical flame.
This article is devoted to the study of a flame ball model, derived by G. Joulin, which satisfies a singular integro-differential equation. We prove that, when radiative heat losses are too important, the flame always quenches; when heat losses are smaller, it stabilizes or quenches, depending on an energy input parameter. We also examine the asymptotics of the radius for these different regimes.
Lyapunov stability solutions of fractional integrodifferential equations.
Mathematical analysis for the peridynamic nonlocal continuum theory
We develop a functional analytical framework for a linear peridynamic model of a spring network system in any space dimension. Various properties of the peridynamic operators are examined for general micromodulus functions. These properties are utilized to establish the well-posedness of both the stationary peridynamic model and the Cauchy problem of the time dependent peridynamic model. The connections to the classical elastic models are also provided.
Mathematical analysis for the peridynamic nonlocal continuum theory*
We develop a functional analytical framework for a linear peridynamic model of a spring network system in any space dimension. Various properties of the peridynamic operators are examined for general micromodulus functions. These properties are utilized to establish the well-posedness of both the stationary peridynamic model and the Cauchy problem of the time dependent peridynamic model. The connections to the classical elastic models are also provided.
Maximal monotone model with delay term of convolution.
Maximal regularity for a class of integro-differential equations with infinite delay in Banach spaces
We use Fourier multiplier theorems to establish maximal regularity results for a class of integro-differential equations with infinite delay in Banach spaces. Concrete equations of this type arise in viscoelasticity theory. Results are obtained for periodic solutions in the vector-valued Lebesgue and Besov spaces. An application to semilinear equations is considered.
Method of semidiscretization in time for quasilinear integrodifferential equations.
Multistep methods for coupled second order integro-differential equations: Stability, convergence and error bounds.