Well-posedness in Maxwell systems with distributions of polarization relaxation parameters

Well-posedness in Maxwell systems with distributions of polarization relaxation parameters

We present existence, uniqueness and continuous dependence (with respect to probability distributions on polarization parameters) of solutions in Maxwell systems. This provides a theoretical and computational foundation for associated inverse problems.

Stii Well{posedness for Hyperbolic Systems with Large Relaxation Terms

The Cauchy problem for linear constant{coeecient hyperbolic systems u t + Au x = (1==)Bu is analyzed. Here (1==)Bu is a large relaxation term, and we are mostly interested in the critical case where B has a non{trivial nullspace. A concept of stii well{posedness is introduced that ensures solution estimates independent of 0 < 1. Under suitable assumptions, we prove convergence of the L 2 {solut...

On the well posedness of Robinson Trautman Maxwell solutions

We show that the so called Robinson-Trautman-Maxwell equations do not constitute a well posed initial value problem. That is, the dependence of the solution on the initial data is not continuous in any norm built out from the initial data and a finite number of its derivatives. Thus, they can not be used to solve for solutions outside the analytic domain. PACS numbers 03.30.De, 04.40.Nk

Well-posedness of Hybrid Systems

Global Well-posedness for the Maxwell-klein Gordon

We prove that the critical Maxwell-Klein Gordon equation on R is globally well-posed for smooth initial data which are small in the energy. This reduces the problem of global regularity for large, smooth initial data to precluding concentration of energy.