Bounds for Solutions to a Class of Damped Integrodifferential Equations in Hilbert Space with Applications to the Theory of Nonconducting Material Dielectrics.
SOUTH CAROLINA UNIV COLUMBIA DEPT OF MATHEMATICS AND COMPUTER SCIENCE
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It is shown that the evolution of the electric displacement field in a simple class of holohedral isotropic dielectrics can be modeled by an initial value problem associated with a certain damped linear integrodifferential equation in Hilbert space. By employing logarithmic convexity arguments growth estimates are derived for solutions of this integrodifferential equation which lie in uniformly bounded subsets of the appropriate Hilbert space the results yield both upper and lower bounds for the magnitude of the electric displacement field in the class of isotropic holohedral dielectrics which is modeled by the abstract initial-value problem.
- Theoretical Mathematics
- Electricity and Magnetism