@article{7a55c2b9f4ba4085b9288174885ea6c6,

title = "The generalized Buckley-Leverett and the regularized Buckley-Leverett equations",

abstract = "This paper studies solutions of the generalized Buckley-Leverett (BL) equation with variable porosity and solutions of the regularized BL equation with the Burgers-Benjamin-Bona-Mahony-type regularization. We construct global in time weak solutions to the Cauchy problem and to the initial- and boundary-value problem for the generalized BL equation and global classical solutions for the regularized BL equation. Solutions of the regularized BL equation are shown to converge to the corresponding solution of the generalized BL equation when the coefficient γ of the BBM term and the coefficient ν of the Burgers term obey γ = O(ν2).",

author = "Hong, {John Meng Kai} and Jiahong Wu and Yuan, {Juan Ming}",

note = "Funding Information: Hong was partially supported by the National Science Council of the Republic of China under the Grant No. NSC-99-2115-M-008-006 and by the Center of Mathematics and Theoretical Physics at the National Central University. Wu was partially supported by NSF Grant No. DMS 0907913 and thanks the Mathematics Research Promotion Center, the Center of Mathematics and Theoretical Physics, and the Department of Mathematics at National Central University. Yuan was partially supported by the National Science Council of the Republic of China under the Grant No. NSC 99-2115-M-126-003. Yuan thanks Professor Goong Chen, Professor I-Liang Chern, and Professor Jyh-Hao Lee for their encouragements.",

year = "2012",

month = may,

day = "7",

doi = "10.1063/1.4711133",

language = "???core.languages.en_GB???",

volume = "53",

journal = "Journal of Mathematical Physics",

issn = "0022-2488",

number = "5",

}