Global small amplitude solutions to systems of nonlinear wave equations with multiple speeds
Preprint Series # 688
Katayama, Soichiro and Yokoyama, Kazuyoshi Global small amplitude solutions to systems of nonlinear wave equations with multiple speeds. (2005);
We give a global existence theorem to systems of quasilinear wave equations in three space dimensions, especially for the multiple-speed cases. It covers a wide class of quadratic nonlinearities which may depend on unknowns as well as their first and second derivatives.
Our proof is achieved through total use of pointwise and $L^2$-estimates concerning unknowns and their first and second derivatives.
|Additional Information:||30 copies|
|Uncontrolled Keywords:||quasi-linear wave equation, global existence, null condition|
|Subjects:||35-xx PARTIAL DIFFERENTIAL EQUATIONS|