scholarly journals A Mathematical Model for Transport in Poroelastic Materials with Variable Volume: Derivation, Lie Symmetry Analysis and Examples. Part 2

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 109
Author(s):  
Roman Cherniha ◽  
Vasyl’ Davydovych ◽  
Joanna Stachowska-Pietka ◽  
Jacek Waniewski

The model for perfused tissue undergoing deformation taking into account the local exchange between tissue and blood and lymphatic systems is presented. The Lie symmetry analysis in order to identify its symmetry properties is applied. Several families of steady-state solutions in closed formulae are derived. An analysis of the impact of the parameter values and boundary conditions on the distribution of hydrostatic pressure, osmotic agent concentration and deformation of perfused tissue is provided applying the solutions obtained in examples describing real-world processes.

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 601 ◽  
Author(s):  
Changzhao Li ◽  
Juan Zhang

This paper considers the Lie symmetry analysis of a class of fractional Zakharov-Kuznetsov equations. We systematically show the procedure to obtain the Lie point symmetries for the equation. Accordingly, we study the vector fields of this equation. Meantime, the symmetry reductions of this equation are performed. Finally, by employing the obtained symmetry properties, we can get some new exact solutions to this fractional Zakharov-Kuznetsov equation.


Author(s):  
E. H. El Kinani ◽  
A. Ouhadan

This paper uses Lie symmetry analysis to reduce the number of independent variables of time fractional partial differential equations. Then symmetry properties have been employed to construct some exact solutions.


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