Citation
Casten, Richard Guy (1970) Methods for deriving conservation laws. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:04192012114039484
Abstract
Systematic methods are used to find all possible conservation laws of a given type for certain systems of partial differential equations, including some from fluid mechanics. The necessary and sufficient conditions for a vector to be divergencefree are found in the form of a system of first order, linear, homogeneous partial differential equations, usually overdetermined. Incompressible, inviscid fluid flow is treated in the unsteady twodimensional and steady threedimensional cases. A theorem about the degrees of freedom of partial differential equations, needed for finding conservation laws, is proven. Derivatives of the dependent variables are then included in the divergencefree vectors. Conservation laws for Laplace's equation are found with the aid of complex variables, used also to treat the twodimensional steady flow case when first derivatives are included in the vectors. Conservation laws, depending on an arbitrary number of derivatives, are found for a general first order quasilinear equation in two independent variables, using two differential operators, which are associated with the derivatives with respect to the independent variables. Linear totally hyperbolic systems are then treated using an obvious generalization of the above operators.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  Applied Mathematics 
Degree Grantor:  California Institute of Technology 
Division:  Engineering and Applied Science 
Major Option:  Applied Mathematics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  25 March 1970 
Record Number:  CaltechTHESIS:04192012114039484 
Persistent URL:  http://resolver.caltech.edu/CaltechTHESIS:04192012114039484 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  6948 
Collection:  CaltechTHESIS 
Deposited By:  Benjamin Perez 
Deposited On:  20 Apr 2012 22:00 
Last Modified:  26 Dec 2012 04:42 
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