Volume 4, Issue 3
Large Time Behavior of Solutions to Burgers Equation with a Time Delay

Takayuki Kubo & Yoshihiro Ueda

Commun. Math. Anal. Appl., 4 (2025), pp. 392-418.

Published online: 2025-09

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  • Abstract

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.

  • AMS Subject Headings

35B40, 35Q35

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COPYRIGHT: © Global Science Press

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@Article{CMAA-4-392, author = {Kubo , Takayuki and Ueda , Yoshihiro}, title = {Large Time Behavior of Solutions to Burgers Equation with a Time Delay}, journal = {Communications in Mathematical Analysis and Applications}, year = {2025}, volume = {4}, number = {3}, pages = {392--418}, abstract = {

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.

}, issn = {2790-1939}, doi = {https://doi.org/10.4208/cmaa.2025-0011}, url = {http://global-sci.org/intro/article_detail/cmaa/24335.html} }
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 -

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.

Kubo , Takayuki and Ueda , Yoshihiro. (2025). Large Time Behavior of Solutions to Burgers Equation with a Time Delay. Communications in Mathematical Analysis and Applications. 4 (3). 392-418. doi:10.4208/cmaa.2025-0011
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