Bounds for solutions to ordinary differential equations applied to a singular Cauchy problem
Author:
W. J. Walker
Journal:
Proc. Amer. Math. Soc. 54 (1976), 7379
MSC:
Primary 35M05
MathSciNet review:
0463719
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Abstract: The Cauchy problem , is shown to be unstable by demonstrating that there exists a sequence of solutions which increase indefinitely on a sequence of neighbourhoods of which shrink to zero, while at the same time the initial data is tending to zero. The equation is investigated with the same initial data and in this case it is shown that the sequence of solutions remains bounded on a neighbourhood of which suggests but does not prove that the Cauchy problem for this equation is well posed. The latter result is a consequence of bounds obtained on a neighbourhood of for complexvalued solutions of the ordinary differential equation
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197604637199
PII:
S 00029939(1976)04637199
Keywords:
Cauchy problem,
parabolic degeneracy,
three independent variables,
dependence on initial conditions
Article copyright:
© Copyright 1976
American Mathematical Society
