A note on the propagation of the bulk of a disturbance for a hyperbolic equation

W. A. Day, G. Saccomandi
1999 Quarterly of Applied Mathematics  
1991 Mathematics Subject Classification. Primary 35L15. ©1999 Brown University cp"udx. (4) dt J-OO J -oo J -oo The choice (x) = 1 (-oo < x < oo) yields the equation d dt d [OO d2 roo / audx+-7z / udx = 0, J -oo J-oo + M 4 ~ M^1 ~exP(_Mi)) J (af + g)dx, and, by invoking Gronwall's inequality again, we readily obtain the estimate /OO 2^ /*oo x2udx>--^ / (a/+ 5) da; + 0(1) as t -> 00.
doi:10.1090/qam/1672179 fatcat:tgmgvngv4fcdzh5qnbvjl4supu