Stability of Compressive and Undercompressive Thin Film Traveling Waves
NORTH CAROLINA STATE UNIV AT RALEIGH CENTER FOR RESEARCH IN SCIENTIFIC COMPUTATION
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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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