EXISTENCE AND UNIQUENESS OF SOLUTIONS OF QUASILINEAR WAVE EQUATIONS (II) BY

In this work we prove a result concernig the existence and uniqueness of solutions of quasilinear wave equation and we con-sider also their trivial solutions. We consider the following initial-boundary value problem for the non-linear wave equation in the form u+ f (u) + g (u̇) = 0 in [0, T) × Ω (QL) with initial values u0 = u (0, ·) , u1 = u ̇ (0, ·) and boundary vale null, that is, u (t, x) = 0 on [0, T] × ∂Ω, where 0 < T ≤ ∞ and Ω ⊂ Rn(n ∈ N) is a bounded domain on which the divergent theorem can be applied.( L2 (Ω) , ‖·‖