Remarks on the existence and uniqueness of global decaying solutions of the nonlinear dissipative wave equations
Global existence and uniqueness of solutions decaying at certain rate as \(t\to \infty\) are derived for small initial data to the initial boundary value problem of the nonlinear wave equation of the form: \[ u_{tt}- \Delta u+\sigma (u_ t)+f(u)=0\quad on\quad \Omega \times [0,\infty),\quad u(x,0)=u_ 0,\quad u_ t(x,0)=u_ 1\quad and\quad u|_{\partial \Omega}=0, \] where \(\Omega\) is a bounded domain in \(R^ N\) and \(\sigma\), f are functions like \(\sigma (u_ t)=| u_ t|^ ru_ t,\) \(-1<r<\infty,\) \(f(u)=| u|^{\alpha}u,\) \(\alpha >2/(N-2).\)
scientific article; zbMATH DE number 4144549