... hyperbolicequations and systems in domains with co nical points. These problems with t heDirichlet boundary conditions were investigated in [3-5] in which the unique existence,the regularity and the asymptotic ... constant independent of uN, f and τ. For theterms III and IV, by the Cauchy inequality, we haveIII ≤(μ − ε2)ρ2mμ1+ ε1|uN|20,Qτ+mμ1+ ε1μ− ε2|uNt|20,Qτ, and IV ... C⎛⎜⎜⎝f2Vl2,α()+mj=1gj2Vl+j−122,α()+u2V02,α−l−2m()⎞⎟⎟⎠(4:5)holds with the constant C independent of u, f, gj and t0.Proof. Without generality we assume that the domain Ω coincides with the cone K in the unit ball. Set Ω0={x...