Commun. Math. Anal. Appl., 4 (2025), pp. 392-418.
Published online: 2025-09
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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} }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.