Global existence for quasilinear wave equations exterior to star-shaped regions with inhomogeneous boundary conditions

作者：Xu, Wei^*

来源：Journal of Mathematical Analysis and Applications, 2023, 522(2): 522 (2023) 126990.

DOI：10.1016/j.jmaa.2022.126990

• Global existence
• Null -form wave equations
• Star -shaped
• KSS estimates
• ???
• WeightedL2-estimates

This paper establishes the global existence of classical solutions to systems of nonlinear wave equations with multiple speeds outside star-shaped regions satisfying time-independent inhomogeneous boundary conditions, provided that nonlinear terms obey the null condition. We first prove the existence and uniqueness of stationary solutions. Then we use the space-time estimates for perturbed wave equations in Metcalfe and Sogge (2007) to show that solutions of systems converge to stationary solutions as time goes to infinity.& COPY; 2023 Elsevier Inc.

• 单位
  南昌航空大学