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The stability of traveling wave solutions of parabolic equations


Hagan, Patrick Shawn (1979) The stability of traveling wave solutions of parabolic equations. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/yn9e-nm19.


A method for determining by inspection the stability or instability of any solution u(t,x) = ɸ(x-ct) of any smooth equation of the form u_t = f(u_(xx),u_x,u where ∂/∂a f(a,b,c) > 0 for all arguments a,b,c, is developed. The connection between the mean wavespeed of solutions u(t,x) and their initial conditions u(0,x) is also explored. The mean wavespeed results and some of the stability results are then extended to include equations which contain integrals and also to include some special systems of equations. The results are applied to several physical examples.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Applied Mathematics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Applied Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Cohen, Donald S.
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 April 1979
Record Number:CaltechTHESIS:03222013-083627751
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7549
Deposited By: Benjamin Perez
Deposited On:25 Mar 2013 15:52
Last Modified:09 Nov 2022 19:20

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