Strain-gradient theory of hydroelastic travelling waves and Young measures of their singular limits

DOI10.1007/s00526-011-0430-yzbMath1243.35180OpenAlexW2049745669MaRDI QIDQ2428580

P. I. Plotnikov, John F. Toland

Publication date: 26 April 2012

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-011-0430-y

zbMATH Keywords

Young measuresfree-boundary problemelastic sheethydroelastic travelling wavessequence of maximizers

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Singular perturbations in context of PDEs (35B25) Free boundary problems for PDEs (35R35) PDEs in connection with mechanics of deformable solids (35Q74) Traveling wave solutions (35C07)

Related Items

The Peskin problem with viscosity contrast ⋮ Well-posedness of the free boundary problem for incompressible elastodynamics ⋮ Variational problems in the theory of hydroelastic waves ⋮ Phase transitions with a minimal number of jumps in the singular limits of higher order theories

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Steady periodic hydroelastic waves
• Bifurcation and secondary bifurcation of heavy periodic hydroelastic travelling waves
• Phase transitions with a minimal number of jumps in the singular limits of higher order theories
• Dual reciprocal states in finite elasticity
• Necessary conditions in the calculus of variations
• Generalized curves
• Necessary conditions in generalized-curve problems of the calculus of variations
• Existence theorems for Bolza problems in the calculus of variations
• Steady periodic water waves under nonlinear elastic membranes
• Nonlinear problems of elasticity