Local well-posedness of a quasilinear wave equation

Abstract

We study a quasilinear wave equation on a domain arising in nonlinear optics. We show local well-posedness for strong solutions using Kato’s approach to quasilinear evolution equations.

Keywords:

• Quasilinear wave equation
• Kerr nonlinearity
• Kato’s method
• Kato stability
• operator semigroups

AMS Subject Classifications:

• Primary: 35L72
• Secondary: 47D06

Notes

No potential conflict of interest was reported by the authors.

1 One can surely lower this regularity to for , but to focus on the main difficulties we avoid fractional Sobolev spaces.

Additional information

Funding

This work was supported by the Deutsche Forschungsgemeinschaft in the framework of the Research Training Group 1294.