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 - <div style="text-align: justify;">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.</div>