Estimates for the characteristic problem of the first-order reduction of the wave equation
Journal of Physics A: Mathematical and General
We calculate certain estimates for the solution of the characteristic problem of the wave equation reduced to first order, in terms of the free data prescribed on two transverse surfaces, one of which is characteristic. Estimates of such kind ensure the stability of the solutions under small variations of the data. Similar estimates exist for the derivatives of the solution as well.
Frittelli, S. (2004). Estimates for the characteristic problem of the first-order reduction of the wave equation. Journal of Physics A: Mathematical and General, 37 (36), 8639-8655. https://doi.org/10.1088/0305-4470/37/36/005