Existence and Uniqueness of Solutions of Quasilinear Wave Equations (ii)
نویسنده
چکیده
In this work we prove a result concernig the existence and uniqueness of solutions of quasilinear wave equation and we consider also their trivial solutions. We consider the following initial-boundary value problem for the nonlinear wave equation in the form u+ f (u) + g (u̇) = 0 in [0, T ) × Ω (QL) with initial values u0 = u (0, ·) , u1 = u̇ (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.
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