Journal of the Mathematical Society of Japan

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


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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 ε 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.

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

First available in Project Euclid: 24 March 2008

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Zentralblatt MATH identifier

Primary: 35L70: Nonlinear second-order hyperbolic equations
Secondary: 49J40: Variational methods including variational inequalities [See also 47J20] 49Q15: Geometric measure and integration theory, integral and normal currents [See also 28A75, 32C30, 58A25, 58C35]

hyperbolic equations linear approximation BV functions minimizing movements varifolds


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.

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