Applications of Mathematics, Vol. 68, No. 5, pp. 643-660, 2023
Spatial decay estimates for the Forchheimer fluid equations in a semi-infinite cylinder
Xuejiao Chen, Yuanfei Li
Received August 22, 2022. Published online December 7, 2022.
Abstract: The spatial behavior of solutions is studied in the model of Forchheimer equations. Using the energy estimate method and the differential inequality technology, exponential decay bounds for solutions are derived. To make the decay bounds explicit, we obtain the upper bound for the total energy. We also extend the study of spatial behavior of Forchheimer porous material in a saturated porous medium.
Keywords: spatial behavior; Forchheimer equations; energy estimate bounds; upper bound; porous medium
Affiliations: Xuejiao Chen (corresponding author), Yuanfei Li, School of Data Science, Guangzhou Huashang College, Zengcheng Street, Guangzhou, Guangdong 511300, P. R. China, e-mail: A10314063@163.com, firstname.lastname@example.org