Almost global existence for quasilinear wave equations with inhomogeneous terms in 3D
-
Yi Zhou
and
Wei Xu
Abstract
This article establishes the almost global existence of solutions for three-dimensional nonlinear wave equations with quadratic, divergence-form nonlinearities and time-independent inhomogeneous terms. The approach used here can be applied to the system of homogeneous, isotropic hyperelasticity with time-independent external force. The development for the scalar and vector cases will be presented in parallel. We first prove the existence and uniqueness of the stationary solutions. Then it suffices to prove the almost global existence of the original solutions minus the stationary solutions, which is carried out in line with Klainerman and Sideris [Comm. Pure Appl. Math. 49: 307–321, 1996], by using the classical invariance of the equations under translations, rotations and changes of scale.
© de Gruyter 2011
Articles in the same Issue
- Almost global existence for quasilinear wave equations with inhomogeneous terms in 3D
- Heegner points and Eisenstein series
- Discrete components of some complementary series
- Even universal binary Hermitian lattices over imaginary quadratic fields
- Combinatorial classification of piecewise hereditary algebras
- Weighted energy estimates for wave equations in exterior domains
- Invariant sets and ergodic decomposition of local semi-Dirichlet forms
- Regularity in parabolic Dini continuous systems
- The reciprocity law for the twisted second moment of Dirichlet L-functions
Articles in the same Issue
- Almost global existence for quasilinear wave equations with inhomogeneous terms in 3D
- Heegner points and Eisenstein series
- Discrete components of some complementary series
- Even universal binary Hermitian lattices over imaginary quadratic fields
- Combinatorial classification of piecewise hereditary algebras
- Weighted energy estimates for wave equations in exterior domains
- Invariant sets and ergodic decomposition of local semi-Dirichlet forms
- Regularity in parabolic Dini continuous systems
- The reciprocity law for the twisted second moment of Dirichlet L-functions
