A problem with parameter for the integro-differential equations
Mathematical Modelling and Analysis, 2021 The article proposes a numerically approximate method for solving a boundary value problem for an integro-differential equation with a parameter and considers its convergence, stability, and accuracy. The integro-differential equation with a parameter is
Elmira A. Bakirova +2 more
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Localized direct boundary-domain integro-differential formulations for incremental elasto-plasticity of inhomogeneous body [PDF]
, 2006 A quasi-static mixed boundary value problem of incremental elasto-plasticity for a continuously inhomogeneous body is considered. Using the two-operator Green–Betti formula and the fundamental solution of a reference homogeneous linear elasticity problem,
Mikhailov, SE
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Periodic solution for a delay integro-differential equation in biomathematics [PDF]
, 2003 Sufficient conditions for the existence and uniqueness of periodic solution of a delay integro-differential equation which arise in biomathematics are given.
Bica, Alexandru Mihai, Muresan, Sorin
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Localized direct boundary–domain integro–differential formulations for scalar nonlinear boundary-value problems with variable coefficients [PDF]
, 2005 Mixed boundary-value Problems (BVPs) for a second-order quasi-linear elliptic partial differential equation with variable coefficients dependent on the unknown solution and its gradient are considered.
Mikhailov, SE
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On Solvability of Integro-Differential Equations [PDF]
Potential Analysis, 2020 AbstractA class of (possibly) degenerate integro-differential equations of parabolic type is considered, which includes the Kolmogorov equations for jump diffusions. Existence and uniqueness of the solutions are established in Bessel potential spaces and in Sobolev-Slobodeckij spaces.
Marta De León-Contreras +2 more
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Neural Integro-Differential Equations
Proceedings of the AAAI Conference on Artificial Intelligence, 2023 Modeling continuous dynamical systems from discretely sampled observations is a fundamental problem in data science. Often, such dynamics are the result of non-local processes that present an integral over time. As such, these systems are modeled with Integro-Differential Equations (IDEs); generalizations of differential equations that comprise both an
Emanuele Zappala +6 more
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On the integro‐differential equations with reflection
Mathematical Methods in the Applied Sciences, 2020 In this paper, by developing important properties on the composition of functions with reflection, using some exponential dichotomy properties and an application of the fixed‐point theorem, several new sufficient conditions for the existence and the uniqueness of an pseudo almost automorphic solutions with measure for some general‐type reflection ...
El Hadi Ait Dads +2 more
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Direct localized boundary-domain integro-differential formulations for physically nonlinear elasticity of inhomogeneous body [PDF]
, 2005 A static mixed boundary value problem (BVP) of physically nonlinear elasticity for a continuously inhomogeneous body is considered. Using the two-operator Green-Betti formula and the fundamental solution of an auxiliary linear operator, a non-standard ...
Mikhailov, SE
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Incremental localized boundary-domain integro-differential equations of elastic damage mechanics for inhomogeneous body [PDF]
, 2006 Copyright @ 2006 Tech Science PressA quasi-static mixed boundary value problem of elastic damage mechanics for a continuously inhomogeneous body is considered.
Mikhailov, SE
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On Pantograph Integro-Differential Equations
Journal of Integral Equations and Applications, 1994 The authors study the initial value problem for pantograph integro- differential equations of the form \[ y'(t) = a y(t) + \int^ 1_ 0 y(qt) d \mu (q) + \int^ 1_ 0 y'(qt) d \nu (q),\;t > 0, \quad y(0) = y_ 0, \tag{1} \] where \(a\) is a complex constant, \(\mu (q)\) and \(\nu (q)\) are complex-valued functions of bounded variation on \([0,1]\). Denote \(
Iserles, Arieh, Liu, Yunkang
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