A varifold solution to the nonlinear equation of motion of a vibrating membrane

DOI10.2996/KMJ/1138037153zbMath0631.49019OpenAlexW2119445031MaRDI QIDQ1094669

Daisuke Fujiwara, Shyôichiro Takakuwa

Publication date: 1986

Published in: Kodai Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2996/kmj/1138037153

zbMATH Keywords

geometric measure theoryvarifoldsBV- solutionsminimal surface-wave-equation

Mathematics Subject Classification ID

Vibrations in dynamical problems in solid mechanics (74H45) Variational problems in a geometric measure-theoretic setting (49Q20) Second-order nonlinear hyperbolic equations (35L70) Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Length, area, volume, other geometric measure theory (28A75) Absolutely continuous real functions of several variables, functions of bounded variation (26B30)

Related Items (2)

Linear approximation for equations of motion of vibrating membrane with one parameter ⋮ Constructing weak solutions in a direct variational method and an application of varifold theory

Cites Work

• Convergence of approximate solutions to conservation laws
• A varifold solution of the nonlinear wave equation of a membrane
• Local existence of \(C^{\infty}\)-solution for the initial-boundary value problem of fully nonlinear wave equation
• On the first variation of a varifold
• A general form of the covering principle and relative differentiation of additive functions
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