Espaces de Sobolev et équations hyperboliques sur des variétés riemanniennes
The present paper studies the existence and uniqueness of global solutions and decay rates to a given nonlinear hyperbolic problem.
The existence and uniqueness of classical global solution and blow up of non-global solution to the first boundary value problem and the second boundary value problem for the equation are proved. Finally, the results of the above problem are applied to the equation arising from nonlinear waves in elastic rods