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.
Publié le : 2008-01-15
Classification:
hyperbolic equations,
linear approximation,
BV functions,
minimizing movements,
varifolds,
35L70,
49J40,
49Q15
@article{1206367958,
author = {KIKUCHI, Koji},
title = {Linear approximation for equations of motion of vibrating membrane with one parameter},
journal = {J. Math. Soc. Japan},
volume = {60},
number = {1},
year = {2008},
pages = { 127-169},
language = {en},
url = {http://dml.mathdoc.fr/item/1206367958}
}
KIKUCHI, Koji. Linear approximation for equations of motion of vibrating membrane with one parameter. J. Math. Soc. Japan, Tome 60 (2008) no. 1, pp. 127-169. http://gdmltest.u-ga.fr/item/1206367958/