A stability theorem for a real analytic singular Cauchy problem

Walker, W. J.

doi:10.1090/S0002-9939-1974-0342877-9

A stability theorem for a real analytic singular Cauchy problem
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by W. J. Walker

Proc. Amer. Math. Soc. 42 (1974), 495-500

DOI: https://doi.org/10.1090/S0002-9939-1974-0342877-9

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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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