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The report is of a mathematical study of electromagnetic phenomena associated with nonlinear dielectrics having memory. Definite details are available in the scientific papers produced and in the SIAM monograph, 'Ill-posed Problems for Integrodifferential Equations in Mechanics and Electromagnetic Theory,' SIAM Studies in Applied Mathematics, August 1981. The basic thrust of the work has been the derivation of stability and growth estimates (in suitable function space norms) for both electric fields and electric induction fields in nonconducting dielectrics with memory. (Author)

Coupled nonlinear wave equations are derived for the evolution of the components of the electric induction field D in a class of rigid nonlinear dielectrics governed by the nonlinear constitutive relation E = lambda (D)D, where E is the electric field and lambda greater than 0 is a scalar-valued vector function. For the special case of a finite one-dimensional dielectric rod, embedded in a perfect conductor, and subjected to an applied electric field, which is perpendicular to the axis of the rod, and depends only on variations of the coordinate along that axis, it is shown that, under relatively mild conditions on lambda, solutions of the corresponding initial-boundary value problem for the electric induction field can not exist globally in time in the L(2) sense; under slightly stronger assumptions on the constitutive function lambda, a standard Riemann Invariant argument may be applied to show that the space-time gradient of the non-zero component of the electric induction field must blow-up in finite time. Some growth estimates for solutions, which are valid on the maximal time-interval of existence are also derived.

Coupled nonlinear wave equations are derived for the evolution of the components of the electric induction field equivalent D in a class of rigid nonlinear dielectrics governed by the nonlinear constitutive relation equivalent E = Lambda (d) equivalent D, where equivalent E is the electric field and Lambda 0 is a scalar-valued vector function. For the special case of an infinite one-dimensional dielectric rod, embedded in a perfect conductor, it is shown that, under relatively mild conditions on Lambda, solutions of the corresponding initial-boundary value problem for the electric induction field cannot exist globally in time in L2 sense if it is assumed that the electric field in the rod is perpendicular to the axis of the rod and varies as the coordinate along that axis. (Author)

Employing results derived for solutions of an abstract integrodifferential equation in Hilbert space, stability and growth estimates are obtained for electric fields in nonconducting material dielectrics. It is assumed that a linear constitutive equation of Maxwell-Hopkinson type relates the electric displacement field in the dielectric; specific results for a simple memory function of exponential type are given.