Osaka Journal of Mathematics
- Osaka J. Math.
- Volume 43, Number 2 (2006), 283-326.
Global small amplitude solutions to systems of nonlinear wave equations with multiple speeds
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.
Osaka J. Math., Volume 43, Number 2 (2006), 283-326.
First available in Project Euclid: 6 July 2006
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35L70: Nonlinear second-order hyperbolic equations
Secondary: 35L05: Wave equation 35L15: Initial value problems for second-order hyperbolic equations 35L55: Higher-order hyperbolic systems
Katayama, Soichiro; Yokoyama, Kazuyoshi. Global small amplitude solutions to systems of nonlinear wave equations with multiple speeds. Osaka J. Math. 43 (2006), no. 2, 283--326. https://projecteuclid.org/euclid.ojm/1152203942