Proceedings of the Japan Academy, Series A, Mathematical Sciences

A remark on parametric resonance for wave equations with a time periodic coefficient

Hideo Ueda

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Abstract

The Cauchy problem for a wave equation with a time periodic coefficient is considered. We prove that if one of the initial data is a compactly supported smooth function and the other initial data is zero, then the energy of the solution of the Cauchy problem grows exponentially. This result is proved by applying the unstable properties of Hill’s equation.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 87, Number 8 (2011), 128-129.

Dates
First available in Project Euclid: 3 October 2011

Permanent link to this document
https://projecteuclid.org/euclid.pja/1317647393

Digital Object Identifier
doi:10.3792/pjaa.87.128

Mathematical Reviews number (MathSciNet)
MR2843092

Zentralblatt MATH identifier
1235.35028

Subjects
Primary: 35L15: Initial value problems for second-order hyperbolic equations 34C11: Growth, boundedness 35B34: Resonances

Keywords
Energy Hill’s equation initial value problems resonances wave equations

Citation

Ueda, Hideo. A remark on parametric resonance for wave equations with a time periodic coefficient. Proc. Japan Acad. Ser. A Math. Sci. 87 (2011), no. 8, 128--129. doi:10.3792/pjaa.87.128. https://projecteuclid.org/euclid.pja/1317647393


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References

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