Decay of solutions of some nonlinear wave equations

$L^p$-decay of solutions to dissipative-dispersive perturbations of conservation laws

“…In the case of the equations (1.1) and (1.2), the maximum principle mentioned above usually fails, hence it is necessary to use different techniques in order to get boundedness of the norm |u(·, t)| 1 for t ≥ 0. This bound seems to be crucial in the proof of the decay of solutions to (1.1) and (1.2), as observed in [4,Lemma 5 [7]. We extend those results to general f and other L p -norms of u.…”

Asymptotic behavior of solutions for the time-delayed equations of Benjamin-Bona-Mahony’s type

“…2 College of Mathematics and Software Science, Sichuan Normal University, Chengdu, 610066, China. 3 School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China.…”

Zero-Dissipation Limit for Nonlinear Waves

“…The following results of Bona et al [8] and Kenig et al [24] serve our purpose nicely. (1) or in case (2) if the data is small. In all the above cases, the solution u depends continuously on u 0 in the exhibited function classes.…”