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Volume 37, Issue 1
On Linear Homogeneous Biwave Equations

Yaqian Bai

DOI: 10.4208/jpde.v37.n1.4

J. Part. Diff. Eq., 37 (2024), pp. 59-87.

Published online: 2024-02

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  • Abstract
The biwave maps are a class of fourth order hyperbolic equations. In this paper, we are interested in the solution formulas of the linear homogeneous biwave equations. Based on the solution formulas and the weighted energy estimate, we can obtain the $L^\infty(\mathbb R^n)-W^{N,1}(\mathbb R^n)$ and $L^\infty(\mathbb R^n)-W^{N,2}(\mathbb R^n)$ estimates, respectively. By our results, we find that the biwave maps enjoy some different properties compared with the standard wave equations.
  • Keywords

Biwave maps, Duhamel’s principle, Fourier transform, Cauchy peoblem, deacy estimate.

  • AMS Subject Headings

35L15, 35L72, 35Q75, 35A01

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-37-59, author = {Bai , Yaqian}, title = {On Linear Homogeneous Biwave Equations}, journal = {Journal of Partial Differential Equations}, year = {2024}, volume = {37}, number = {1}, pages = {59--87}, abstract = {
The biwave maps are a class of fourth order hyperbolic equations. In this paper, we are interested in the solution formulas of the linear homogeneous biwave equations. Based on the solution formulas and the weighted energy estimate, we can obtain the $L^\infty(\mathbb R^n)-W^{N,1}(\mathbb R^n)$ and $L^\infty(\mathbb R^n)-W^{N,2}(\mathbb R^n)$ estimates, respectively. By our results, we find that the biwave maps enjoy some different properties compared with the standard wave equations.
}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v37.n1.4}, url = {http://global-sci.org/intro/article_detail/jpde/22906.html} }
TY - JOUR T1 - On Linear Homogeneous Biwave Equations AU - Bai , Yaqian JO - Journal of Partial Differential Equations VL - 1 SP - 59 EP - 87 PY - 2024 DA - 2024/02 SN - 37 DO - http://doi.org/10.4208/jpde.v37.n1.4 UR - https://global-sci.org/intro/article_detail/jpde/22906.html KW - Biwave maps, Duhamel’s principle, Fourier transform, Cauchy peoblem, deacy estimate. AB -
The biwave maps are a class of fourth order hyperbolic equations. In this paper, we are interested in the solution formulas of the linear homogeneous biwave equations. Based on the solution formulas and the weighted energy estimate, we can obtain the $L^\infty(\mathbb R^n)-W^{N,1}(\mathbb R^n)$ and $L^\infty(\mathbb R^n)-W^{N,2}(\mathbb R^n)$ estimates, respectively. By our results, we find that the biwave maps enjoy some different properties compared with the standard wave equations.
Yaqian Bai. (2024). On Linear Homogeneous Biwave Equations. Journal of Partial Differential Equations. 37 (1). 59-87. doi:10.4208/jpde.v37.n1.4
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