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dc.contributor.authorLaugesen, Richard S. ( Orcid Icon 0000-0003-1106-7203 )
dc.contributor.authorPugh, Mary C. ( )
dc.identifier.citationLaugesen, R. S., & Pugh, M. C. (2002). Heteroclinic orbits, mobility parameters and stability for thin film type equations. Electronic Journal of Differential Equations, 2002(95), pp. 1-29.en_US

We study the phase space of the evolution equation

ht = -(hnhxxx)x - B(hmhx)x,

where h(x, t) ≥ 0. The parameters n > 0, m ∈ ℝ, and the Bond number B > 0 are given. We find numerically, for some ranges of n and m, that perturbing the positive periodic steady state in a certain direction yields a solution that relaxes to the constant steady state. Meanwhile perturbing in the opposite direction yields a solution that appears to touch down or 'rupture' in finite time, apparently approaching a compactly supported 'droplet' steady state. We then investigate the structural stability of the evolution by changing the mobility coefficients, hn and hm. We find evidence that the above heteroclinic orbits between steady states are perturbed but not broken, when the mobilities are suitably changed. We also investigate touch-down singularities, in which the solution changes from being everywhere positive to being zero at isolated points in space. We find that changes in the mobility exponent n can affect the number of touch-down points per period, and affect whether these singularities occur in finite or infinite time.

dc.format.extent29 pages
dc.format.medium1 file (.pdf)
dc.publisherSouthwest Texas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2002, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectNonlinear PDE of parabolic typeen_US
dc.subjectHeteroclinic orbitsen_US
dc.subjectStability problemsen_US
dc.subjectLubrication theoryen_US
dc.titleHeteroclinic Orbits, Mobility Parameters and Stability for Thin Film Type Equationsen_US
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.



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