An existence result of the Cauchy Dirichlet problem for the Hermite heat equation

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An existence result of the Cauchy Dirichlet problem for the Hermite heat equation

Bishnu Prasad Dhungana and Tadato Matsuzawa

Source: Proc. Japan Acad. Ser. A Math. Sci. Volume 86, Number 2 (2010), 45-47.

Abstract

Using the Mehler kernel, we give an existence result of the Cauchy Dirichlet problem for the Hermite heat equation with homogeneous Dirichlet boundary conditions and continuous and bounded Cauchy data vanishing at x=0.

Primary Subjects: 33C45

Secondary Subjects: 35K15

Keywords: Hermite functions; Mehler kernel; Hermite heat equation; Cauchy Dirichlet problem

Full-text: Open access

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.pja/1265033222
Digital Object Identifier: doi:10.3792/pjaa.86.45
Zentralblatt MATH identifier: 05690875
Mathematical Reviews number (MathSciNet): MR2590200

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References

[1]H. S. Carslaw and J. C Jager, Conduction of heat in solids, Second edition, Oxford University Press, 1976.

[2]B. P. Dhungana, An example of nonuniqueness of the Cauchy problem for the Hermite heat equation, Proc. Japan Acad. Ser. A Math. Sci. 81 (2005), no. 3, 37-39.

Mathematical Reviews (MathSciNet): MR2128928

Digital Object Identifier: doi:10.3792/pjaa.81.37

Project Euclid: euclid.pja/1116442033

[3]B. P. Dhungana, Mehler kernel approach to tempered distributions, Tokyo J. Math. 29 (2006), no. 2, 283-293.

Mathematical Reviews (MathSciNet): MR2284972

Zentralblatt MATH: 1120.33007

Digital Object Identifier: doi:10.3836/tjm/1170348167

Project Euclid: euclid.tjm/1170348167

[4]B. P. Dhungana, S.-Y. Chung and D. Kim, Characterization of Fourier hyperfunctions by solutions of the Hermite heat equation, Integral Transforms Spec. Funct. 18 (2007), no. 7-8, 471-480.

Mathematical Reviews (MathSciNet): MR2348591

Digital Object Identifier: doi:10.1080/10652460701320729

[5]F. John, Partial differential equations, Third edition, Springer, New York, 1978.

Mathematical Reviews (MathSciNet): MR514404

[6]N. V. Krylov, Lectures on elliptic and parabolic equations in Hölder spaces, Amer. Math. Soc., Providence, RI, 1996.

Mathematical Reviews (MathSciNet): MR1406091

[7]D. V. Widder, The heat equation, Academic Press, New York, 1975.

Mathematical Reviews (MathSciNet): MR466967

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