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

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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 ℝn 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 ℝn. The authors show that these weighted L2-estimates are closely related to the geometrical properties of the metric g = A−1(x).

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Authors and Affiliations

  1. Key Laboratory of Control and System, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Pengfei Yao

  2. Department of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, China

    Zhifei Zhang

Authors
  1. Pengfei Yao
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  2. Zhifei Zhang
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Corresponding author

Correspondence to Zhifei Zhang.

Additional information

The work was supported by the National Science Foundation of China under Grant Nos. 61573342, 61473126, the Key Research Program of Frontier Sciences, Chinese Academy of Sciences, under Grant No. QYZDJ-SSWSYS011 and the Fundamental Research Funds for the Central Universities.

This paper was recommended for publication by Editor SUN Jian.

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Yao, P., Zhang, Z. Weighted L2-estimates of solutions for damped wave equations with variable coefficients. J Syst Sci Complex 30, 1270–1292 (2017). https://doi.org/10.1007/s11424-017-6093-9

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  • DOI: https://doi.org/10.1007/s11424-017-6093-9

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