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Journal of Systems Science and Complexity

, Volume 30, Issue 6, pp 1270–1292 | Cite as

Weighted L2-estimates of solutions for damped wave equations with variable coefficients

  • Pengfei Yao
  • Zhifei ZhangEmail author
Article
  • 82 Downloads

Abstract

The authors establish weighted L2-estimates of solutions for the damped wave equations with variable coefficients u tt − divA(x)∇u+au t = 0 in n under the assumption a(x) ≥ a0[1+ρ(x)]l, where a0 > 0, l < 1, ρ(x) is the distance function of the metric g = A−1(x) on n . The authors show that these weighted L2-estimates are closely related to the geometrical properties of the metric g = A−1(x).

Keywords

Distance function of a metric Riemannian metric wave equation with variable coefficients weighted L2-estimate 

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Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Key Laboratory of Control and System, Institute of Systems Science, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina
  2. 2.Department of Mathematics and StatisticsHuazhong University of Science and TechnologyWuhanChina

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