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An example of nonuniqueness of the Cauchy problem
Bishnu P. Dhungana
Source: Proc. Japan Acad. Ser. A Math. Sci. Volume 81, Number 3
(2005), 37-39.
Abstract
Using Mehler kernel, we give an example of nontrivial solution of the homogeneous Cauchy problem of the Hermite heat equation, which is, for each $t$, bounded in the space variables.
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33R45
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Permanent link to this document: http://projecteuclid.org/euclid.pja/1116442033
Mathematical Reviews number (MathSciNet): MR2128928
Zentralblatt MATH identifier: 05009464
Digital Object Identifier: doi:10.3792/pjaa.81.37
References
W. Bodanko, Sur le problème de Cauchy et les problèmes de Fourier pour les équations paraboliques dans un domaine non borné, Ann. Polon. Math. 18 (1966), 79--94.
Mathematical Reviews (MathSciNet): MR197998
S.-Y. Chung, Uniqueness in the Cauchy problem for the heat equation, Proc. Edinburgh Math. Soc. (2) 42 (1999), no. 3, 455--468.
Mathematical Reviews (MathSciNet): MR1721765
S.-Y. Chung and D. Kim, An example of nonuniqueness of the Cauchy problem for the heat equation, Comm. Partial Differential Equations 19 (1994), no. 7-8, 1257--1261.
Mathematical Reviews (MathSciNet): MR1284810
J. Rauch, Partial differential equations, Springer, New York, 1991.
Mathematical Reviews (MathSciNet): MR1223093
Zentralblatt MATH: 0742.35001
E. T. Whittaker and G. N. Watson, A course of modern analysis, Cambridge University Press, Cambridge, 1935.
Mathematical Reviews (MathSciNet): MR1424469
M. W. Wong, Weyl transforms, Springer, New York, 1998.
Mathematical Reviews (MathSciNet): MR1639461
Zentralblatt MATH: 0908.44002
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Proceedings of the Japan Academy, Series A, Mathematical Sciences
