Almost global existence for quasilinear wave equations with inhomogeneous terms in 3D

作者：Zhou Yi^*; Xu Wei

来源：Forum Mathematicum, 2011, 23(6): 1113-1134.

DOI：10.1515/FORM.2011.039

• Almost global existence
• inhomogeneous terms
• stationary solutions
• weighted L-2-estimates
• generalized energy method

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 [8], by using the classical invariance of the equations under translations, rotations and changes of scale.

• 出版日期2011-11
• 单位复旦大学