scholarly journals A GROUP CLASSIFICATION OF A SYSTEM OF PARTIAL DIFFERENTIAL EQUATIONS MODELING FLOW IN COLLAPSIBLE TUBES

2009 ◽  
Vol 16 (sup1) ◽  
pp. 179-208 ◽  
Author(s):  
M. MOLATI ◽  
F. M. MAHOMED ◽  
C. WAFO SOH
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Group Classification ◽  
Partial Differential ◽  
Collapsible Tubes ◽  
Modeling Flow

scholarly journals GROUP PROPERTIES OF A ONE-DIMENSIONAL NONLINEAR POROELASTICITY EQUATION

2019 ◽  
Vol 4 (1) ◽  
pp. 149-155
Author(s):  
Kholmatzhon Imomnazarov ◽  
Ravshanbek Yusupov ◽  
Ilham Iskandarov
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Lie Algebra ◽  
Three Dimensional ◽  
Group Classification ◽  
Second Order ◽  
Partial Differential ◽  
One Dimensional ◽  
Preliminary Group

This paper studies a class of partial differential equations of second order , with arbitrary functions and , with the help of the group classification. The main Lie algebra of infinitely infinitesimal symmetries is three-dimensional. We use the method of preliminary group classification for obtaining the classifications of these equations for a one-dimensional extension of the main Lie algebra.

scholarly journals Classification of Exact Solutions for Generalized Form of Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Hasan Bulut
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Generalized Equation ◽  
Polynomial Method ◽  
Partial Differential ◽  
Elliptic Solutions ◽  
Complete Discrimination System

The classification of exact solutions, including solitons and elliptic solutions, to the generalized equation by the complete discrimination system for polynomial method has been obtained. From here, we find some interesting results for nonlinear partial differential equations with generalized evolution.

Conservation laws and null divergences

1983 ◽  
Vol 94 (3) ◽  
pp. 529-540 ◽  
Author(s):  
Peter J. Olver
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Conservation Laws ◽  
Existence Of Solutions ◽  
Complete Classification ◽  
Complete Analysis ◽  
Partial Differential ◽  
Physical Systems

For a system of partial differential equations, the existence of appropriate conservation laws is often a key ingredient in the investigation of its solutions and their properties. Conservation laws can be used in proving existence of solutions, decay and scattering properties, investigation of singularities, analysis of integrability properties of the system and so on. Representative applications, and more complete bibliographies on conservation laws, can be found in references [7], [8], [12], [19]. The more conservation laws known for a given system, the more tools available for the above investigations. Thus a complete classification of all conservation laws of a given system is of great interest. Not many physical systems have been subjected to such a complete analysis, but two examples can be found in [11] and [14]. The present paper arose from investigations ([15], [16]) into the conservation laws of the equations of elasticity.

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