Stability of Compressive and Undercompressive Thin Film Traveling Waves

Abstract

Recent studies of liquid films driven by competing forces due to surface tension gradients and gravity reveal that undercompressive traveling waves play an important role in the dynamics when the competing forces are comparable. In this paper we provide a theoretical framework for assessing the spectral stability of compressive and undercompressive traveling waves in thin film models. Associated with the linear stability problem is an Evans function which vanishes precisely at eigenvalues of the linearized operator. The structure of an index related to the Evans function explains computational results for stability of compressive waves. A new formula for the index in the undercompressive case yields results consistent with stability.

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Document Details

Document Type
Technical Report
Publication Date
Dec 08, 1999
Accession Number
ADA446038

Entities

People

  • Andrea Bertozzi
  • Andreas Munch
  • Kevin Zumbrun
  • Michael Shearer

Organizations

  • North Carolina State University

Tags

Communities of Interest

  • Advanced Electronics

DTIC Thesaurus Topics

  • Abstracts
  • Films
  • Information Operations
  • North Carolina
  • Surface Tension
  • Thin Films
  • Traveling Waves
  • Waves

Fields of Study

  • Mathematics

Readers

  • Cellular and Molecular Pathways of Apoptosis.
  • Plasma Physics / Magnetohydrodynamics
  • Structural Dynamics.