Analysis and profiles of travelling wave solutions to a Darcy-Forchheimer fluid formulated with a non-linear diffusion

被引:7
|
作者
Rahman, S. [1 ]
Diaz Palencia, J. L. [2 ,3 ]
Roa Gonzalez, J. [2 ]
机构
[1] COMSATS Univ Islamabad, Dept Math, Abbottabad, Pakistan
[2] Univ Distancia Madrid, Via Serv A-6,15, Madrid 28400, Spain
[3] Univ Francisco de Vitoria, Escuela Politecn Super, Ctra Pozuelo Majadahonda Km 1800, Madrid 28223, Spain
来源
AIMS MATHEMATICS | 2022年 / 7卷 / 04期
关键词
existence; uniqueness; asymptotic; travelling waves; Geometric Perturbation Theory; porous media equation; Darcy-Forchheimer; CARBON NANOTUBES; FLOW; MODEL;
D O I
10.3934/math.2022383
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The intention along the presented analysis is to explore existence, uniqueness, regularity of solutions and travelling waves profiles to a Darcy-Forchheimer fluid flow formulated with a non-linear diffusion. Such formulation is the main novelty of the present study and requires the introduction of an appropriate mathematical treatment to deal with the introduced degenerate diffusivity. Firstly, the analysis on existence, regularity and uniqueness is shown upon definition of an appropriate test function. Afterwards, the problem is formulated within the travelling wave domain and analyzed close the critical points with the Geometric Perturbation Theory. Based on this theory, exact and asymptotic travelling wave profiles are obtained. In addition, the Geometric Perturbation Theory is used to provide evidences of the normal hyperbolicity in the involved manifolds that are used to get the associated travelling wave solutions. The main finding, which is not trivial in the non-linear diffusion case, is related with the existence of an exponential profile along the travelling frame. Eventually, a numerical exercise is introduced to validate the analytical solutions obtained.
引用
收藏
页码:6898 / 6914
页数:17
相关论文
共 50 条