Parallel Schwarz waveform relaxation method for a semilinear heat equation in a cylindrical domain

We present here a proof of well-posedness and convergence for the parallel Schwarz waveform relaxation algorithm adapted to the semilinear heat equation in a cylindrical domain. It relies on a careful estimate of a local time of existence thanks to the Banach theorem in a well chosen metric space, together with new cylindrical error estimates.