id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
easat-3857	Tuan, Lai Thanh ; Dung, Nguyen Van ; Tan, Bui Dinh ; Tam, Ta Duc 	Propagation of nonstationary boundary disturbances in a half-plane filled with a homogeneous isotropic elastic medium	2024	13	.pdf	application/pdf	7381	292	70	The functions in (41) and (42) are related to each other and are defined by the following functions as follows: ( ) ( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( ) 2 2 2 2 2 2 21 2 2 1 0 2 2 2 2 2 2 2 22 2 2 1 0 2 4 2 2 2 2 2 21 22 2 2 1 2 3 3 2 6 3 4 2 2 2 3 3 32 2 2 2 2 ( , ) 2 4 ; ( , ) 2 4 ; ( , ) ( , ) 2 16 ( , ); ( , ) 8 8 2 8 1 R x x x x R x R x x x x R x R x R x x x x xP x P x P x x x x                                              = − − − − = = − − − − = = − − − − = = = − + + − + (43) Formulas (40)-(42) finally lead to the following result: ( ) 2 ( ) 30 30 1 ( , ) ( , )k k k u x u x H x    = = − (44) where ( ) ( ) 2 2 2 2 2 1(2) (3) (1) 2 2 2 30 30 30 22 2 3 4 , x u u u x P x         − = − = − (45) At the initial moment of time and at infinity there are no disturbances: 0 0 0 0 0;       	cache/easat-3857.pdf	txt/easat-3857.txt