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A stability theorem for a real analytic singular Cauchy problem


Author: W. J. Walker
Journal: Proc. Amer. Math. Soc. 42 (1974), 495-500
MSC: Primary 35M05
DOI: https://doi.org/10.1090/S0002-9939-1974-0342877-9
MathSciNet review: 0342877
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Abstract: In this paper we prove the equation $ {u_{tt}} - {t^{2p}}{u_{xx}} - a(t){u_x} = 0,p > 0$, with initial conditions $ u(x,0) = \alpha (x),{u_t}(x,0) = \beta (x)$ is well posed provided that $ \alpha (x)$ and $ \beta (x)$ belong to special classes of real analytic functions. In general this problem is not stable for $ p > 1$ and $ \alpha (x)$ and $ \beta (x)$ real analytic functions.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0342877-9
Article copyright: © Copyright 1974 American Mathematical Society

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