$G$-Convergence of Linear Differential Equations
Copyright policy )$G$-Convergence of Linear Differential Equations
We discuss G -convergence of linear integro-differential-algebraic equations in Hilbert spaces. We show under which assumptions it is generic for the limit equation to exhibit memory effects. Moreover, we investigate which classes of equations are closed under the process of G -convergence. The results have applications to the theory of homogenization. As an example we treat Maxwell's equation with the Drude–Born–Fedorov constitutive relation.
- TU Dresden Germany
Linear operator approximation theory, Linear integral equations, integral equations, Applications of operator theory to differential and integral equations, 34L99, 34E13, 34A08, 35B27, 35Q61, 45A05, homogenization, Multiple scale methods for ordinary differential equations, Fractional ordinary differential equations, Functional Analysis (math.FA), Mathematics - Functional Analysis, Ordinary differential operators, Maxwell equations, integro-differential-algebraic equations, Maxwell's equations, FOS: Mathematics, \(G\)-convergence
Linear operator approximation theory, Linear integral equations, integral equations, Applications of operator theory to differential and integral equations, 34L99, 34E13, 34A08, 35B27, 35Q61, 45A05, homogenization, Multiple scale methods for ordinary differential equations, Fractional ordinary differential equations, Functional Analysis (math.FA), Mathematics - Functional Analysis, Ordinary differential operators, Maxwell equations, integro-differential-algebraic equations, Maxwell's equations, FOS: Mathematics, \(G\)-convergence
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