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Bounds for Solutions of Some Non-Linear Parabolic Problems


Dickson, Robert John (1954) Bounds for Solutions of Some Non-Linear Parabolic Problems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/VMCG-3G45.


NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. 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 x-derivatives 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.))
Subject Keywords:(Mathematics and Aeronautics)
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Minor Option:Aeronautics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Bohnenblust, Henri Frederic
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1954
Record Number:CaltechETD:etd-12102003-104645
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4921
Deposited By: Imported from ETD-db
Deposited On:12 Dec 2003
Last Modified:07 Jun 2023 23:41

Thesis Files

PDF (Dickson_rj_1954.pdf) - Final Version
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