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Kikuchi, Koji

Linear approximation for equations of motion of vibrating membrane with one parameter. (English) Zbl 1142.35049

J. Math. Soc. Japan 60, No. 1, 127-169 (2008).
Summary: 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.

Cited in 3 Documents

MSC:

35L70 Second-order nonlinear hyperbolic equations
49J40 Variational inequalities
49Q15 Geometric measure and integration theory, integral and normal currents in optimization
74K15 Membranes

Keywords:

BV functions; minimizing movements; varifolds; d’Alembert equation
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References:

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