TY - JOUR
T1 - Large Time Behavior of Solutions to Burgers Equation with a Time Delay
AU - Kubo , Takayuki
AU - Ueda , Yoshihiro
JO - Communications in Mathematical Analysis and Applications
VL - 3
SP - 392
EP - 418
PY - 2025
DA - 2025/09
SN - 4
DO - http://doi.org/10.4208/cmaa.2025-0011
UR - https://global-sci.org/intro/article_detail/cmaa/24335.html
KW - Burgers equation, time delay, large time behavior.
AB - <p style="text-align: justify;">In this article, we consider the large time behavior of solutions $ρ$ to
the one-dimensional Cauchy problem of the generalized viscous Burgers equations with a time delay. More precisely, we derive the time decay estimate of the
solution to the Cauchy problem, provided by $ρ_0(0)∈L^1$ and $ρ_0∈C([−τ,0];H^1
).$ The result is based on the combination of the weighted $L^2$ energy estimate and
the $L^1$ estimate.</p>