## Journal of the Mathematical Society of Japan

### Linear approximation for equations of motion of vibrating membrane with one parameter

Koji KIKUCHI

#### Abstract

This article treats a one parameter family of equations of motion of vibrating membrane whose energy functionals converge to the Dirichlet integral as the parameter $\varepsilon$ tends to zero. It is proved that both weak solutions satisfying energy inequality and generalized minimizing movements converge to a unique solution to the d’Alembert equation.

#### Article information

Source
J. Math. Soc. Japan, Volume 60, Number 1 (2008), 127-169.

Dates
First available in Project Euclid: 24 March 2008

https://projecteuclid.org/euclid.jmsj/1206367958

Digital Object Identifier
doi:10.2969/jmsj/06010127

Mathematical Reviews number (MathSciNet)
MR2392006

Zentralblatt MATH identifier
1142.35049

#### Citation

KIKUCHI, Koji. Linear approximation for equations of motion of vibrating membrane with one parameter. J. Math. Soc. Japan 60 (2008), no. 1, 127--169. doi:10.2969/jmsj/06010127. https://projecteuclid.org/euclid.jmsj/1206367958

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