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We present in this paper a proof of well-posedness and convergence for theparallel Schwarz Waveform Relaxation Algorithm adapted to an N-dimensionalsemilinear heat equation. Since the equation we study is an evolution one, eachsubproblem at each step has its own local existence time, we then determine acommon existence time for every problem in any subdomain at any step. We alsointroduce a new technique: Exponential Decay Error Estimates, to prove theconvergence of the Schwarz Methods, with multisubdomains, and then apply it toour problem.

Parallel Schwarz Waveform Relaxation Algorithm for an N-Dimensional Semilinear Heat Equation