An optimal-order error estimate on anH1-Galerkin mixed method for a nonlinear parabolic equation in porous medium flow

2010 ◽  
Vol 26 (1) ◽  
pp. 188-205 ◽  
Author(s):  
Huan-Zhen Chen ◽  
Hong Wang
Keyword(s):  
Porous Medium ◽  
Parabolic Equation ◽  
Error Estimate ◽  
Mixed Method ◽  
Nonlinear Parabolic Equation ◽  
Optimal Order ◽  
Order Error ◽  
Nonlinear Parabolic ◽  
Medium Flow ◽  
Porous Medium Flow

scholarly journals $L^{\infty }$ decay estimates of solutions of nonlinear parabolic equation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hui Wang ◽  
Caisheng Chen
Keyword(s):  
Parabolic Equation ◽  
Weak Solutions ◽  
Nonlinear Parabolic Equation ◽  
Divergence Form ◽  
Decay Estimates ◽  
Laplacian Equation ◽  
Estimates Of Solutions ◽  
Nonlinear Parabolic ◽  
Doubly Nonlinear ◽  
Doubly Nonlinear Parabolic Equation

AbstractIn this paper, we are interested in $L^{\infty }$ L ∞ decay estimates of weak solutions for the doubly nonlinear parabolic equation and the degenerate evolution m-Laplacian equation not in the divergence form. By a modified Moser’s technique we obtain $L^{\infty }$ L ∞ decay estimates of weak solutiona.

Duality and stability of MHD Darcy–Forchheimer porous medium flow of rotating nanofluid on a linear shrinking/stretching sheet: Buongiorno model

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Jawad Raza ◽  
Sumera Dero ◽  
Liaquat Ali Lund ◽  
Zurni Omar
Keyword(s):  
Porous Medium ◽  
Stability Analysis ◽  
Differential Equations ◽  
Shrinking Sheet ◽  
Dual Nature ◽  
Content Type ◽  
Great Achievement ◽  
Medium Flow ◽  
Buongiorno Model ◽  
Porous Medium Flow

Purpose The purpose of study is to examine the dual nature of the branches for the problem of Darcy–Forchheimer porous medium flow of rotating nanofluid on a linearly stretching/shrinking surface under the field of magnetic influence. The dual nature of the branches confronts the uniqueness and existence theorem, moreover, mathematically it is a great achievement. For engineering purposes, this study applied a linear stability test on the multiple branches to determine which solution is physically reliable (stable). Design/methodology/approach Nanofluid model has been developed with the help of Buongiorno model. The partial differential equations in space coordinates for the law of conservation of mass, momentum and energy have been transformed into ordinary differential equations by introducing the similarity variables. Two numerical techniques, namely, the shooting method in Maple software and the three-stage Lobatto IIIA method in Matlab software, have been used to find multiple branches and to accomplish stability analysis, respectively. Findings The parametric investigation has been executed to find the multiple branches and explore the effects on skin friction, Sherwood number, Nusselt number, concentration and temperature profiles. The findings exhibited the presence of dual branches only in the case of a shrinking sheet. Originality/value The originality of work is a determination of multiple branches and the performance of the stability analysis of the branches. It has also been confirmed that such a study has not yet been considered in the previous literature.

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