Blow-up for nonlinear Maxwell equations
Texas State University, Department of Mathematics
We construct classical solutions to the nonlinear Maxwell system with periodic boundary conditions which blow up in H(curl). A similar result is shown on the full space. Our construction is based on an analysis of a shock wave in one space dimension.
Quasilinear Maxwell system, Blow-up, Shock, Kerr model
D'Ancona, P., Nicaise, S., & Schnaubelt, R. (2018). Blow-up for nonlinear Maxwell equations. <i>Electronic Journal of Differential Equations, 2018</i>(73), pp. 1-9.