Stability estimates of solutions to ill-posed Cauchy problem for electrodynamics and elasticity equations

Cauchy problem for of electrodynamics and elasticity equations with data on time-like surfaces are considered. Stability estimates for these problems are stated. Moreover, formulae for coefficients of an asymptotic series for a solution to elasticity equations with a point impulse force are given. These coefficients determine a singular part and jumps of the solution across the characteristic surfaces corresponding to compressive and share waves.