Existence of global solutions to the Cauchy problem of Kirchhoff type quasilinear wave equation with weakly nonlinear dissipation

Mitsuhiro Nakao and Jeong Ja Bae
(Kyushu University and Pusan National University)

Funkcialaj Ekvacioj, 45 (2002), 387-395

\begin{displaymath} u(x,0)= u_0(x) \quad\hbox{and}\quad u_t(x,0)= u_1(x), \eqno{(1.2)} \end{displaymath}

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\begin{displaymath} 0 < k_0 \leq \rho'(v) \leq k_1 < \infty \quad\hbox{and}\quad \rho(0)=0. \eqno{(1.3)} \end{displaymath}