Citation
Dickson, Robert John (1954) Bounds for solutions of some nonlinear parabolic problems. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd12102003104645
Abstract
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Functions v(x,t) satisfying certain partial differential equations of the form v[subscript t]=F(x,t,v,v[subscript x],v[subscript xx] in the region R: 0 < x < 1, 0 < t [<=] T are studied. The principal results of Part I determine circumstances in which it can be asserted that v and v[subscript x] admit, in R, bounds which depend only on the bounds for the functions v(x,0), v(0,t), and v(1,t), and for the derivatives of these functions. The proofs employ certain elementary comparison theorems for solutions of partial differential inequalities. Some other applications of these theorems are also included in Part I.
In Part II analogous results are obtained for the system of first order ordinary differential equations which arises when the xderivatives in the partial differential equation are replaced by divided differences. The bounds obtained in this case hold uniformly under refinement of the discretization.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Degree Grantor:  California Institute of Technology 
Division:  Physics, Mathematics and Astronomy 
Major Option:  Mathematics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  1 January 1954 
Record Number:  CaltechETD:etd12102003104645 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd12102003104645 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  4921 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  12 Dec 2003 
Last Modified:  26 Dec 2012 03:12 
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