Some regularity results for quasilinear parabolic systems
We give examples of parabolic systems (in space dimension ) having a solution with real analytic initial and boundary values which develops the discontinuity in the interior of the parabolic cylinder.
We discuss the propagation of electromagnetic waves of a special form through an inhomogeneous isotropic medium which has a cylindrical symmetry and a nonlinear dielectric response. For the case where this response is of self-focusing type the problem is treated in [1]. Here we continue this study by dealing with a defocusing dielectric response. This tends to inhibit the guidance properties of the medium and so guidance can only be expected provided that the cylindrical stratification is such that...
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