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Electrostatic Boundary Value Problems Involving Laplacian Fields
Published in Ahmad Shahid Khan, Saurabh Kumar Mukerji, Electromagnetic Fields, 2020
Ahmad Shahid Khan, Saurabh Kumar Mukerji
The Uniqueness Theorem states: If a solution exists for a given equation under certain specified boundary conditions, it is the only possible solution and may be referred to as unique.
Constructive solution of the inverse spectral problem for the matrix Sturm–Liouville operator
Published in Inverse Problems in Science and Engineering, 2020
Inverse problems of spectral analysis consist in reconstruction of operators, by using their spectral information. The most complete results in inverse problem theory are obtained for scalar Sturm–Liouville operators (see the monographs [8–11]). Analysis of an inverse spectral problem usually includes the following steps: Uniqueness theorem.Constructive solution.Necessary and sufficient conditions of solvability.Local solvability and stability.Numerical methods.
Attractors of Ginzburg–Landau equations with oscillating terms in porous media: homogenization procedure
Published in Applicable Analysis, 2023
Kuanysh A. Bekmaganbetov, Gregory A. Chechkin, Abylaikhan A. Tolemis
Finally, we consider the Ginzburg–Landay equation for which the uniqueness theorem of the Cauchy problem takes place. It is sufficient to assume that the function in Equation (8) satisfies the condition (9) with the constant . In this case Equations (8) and (25) generate the dynamical semigroups in which have the global attractors and , bounded in the space (see [26–30]). We have Convergence (46) implies
Weak convergence of attractors of reaction–diffusion systems with randomly oscillating coefficients
Published in Applicable Analysis, 2019
Kuanysh A. Bekmaganbetov, Gregory A. Chechkin, Vladimir V. Chepyzhov
Finally we consider the reaction diffusion systems for which the uniqueness theorem of the Cauchy problem takes place. It is sufficient to assume that the nonlinear term f(u) in the Equation (13) satisfies the condition (see [15,46]). In [46] it was proved that if (36) holds, then Equations (13) and (22) generate the dynamical semigroups in which have the global attractors and bounded in the space (see also [14,16]). We have