×

An example of nonuniqueness of the Cauchy problem for the Hermite heat equation. (English) Zbl 1091.35030

Summary: 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.

MSC:

35K15 Initial value problems for second-order parabolic equations
35K05 Heat equation
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
PDFBibTeX XMLCite
Full Text: DOI Euclid

References:

[1] 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. · Zbl 0139.05504
[2] S.-Y. Chung, Uniqueness in the Cauchy problem for the heat equation, Proc. Edinburgh Math. Soc. (2) 42 (1999), no. 3, 455-468. · Zbl 0945.35040
[3] 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. · Zbl 0810.35031
[4] J. Rauch, Partial differential equations , Springer, New York, 1991. · Zbl 0742.35001
[5] E. T. Whittaker and G. N. Watson, A course of modern analysis , Cambridge University Press, Cambridge, 1935. · JFM 45.0433.02
[6] M. W. Wong, Weyl transforms , Springer, New York, 1998. · Zbl 0908.44002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.