In one space dimension, we study the finite speed of propagation property for zero contact--angle solutions of the thin-film equation in presence of a convective term. In the case of strong slippage, we obtain bounds in terms of the initial mass for both the ``fast" and the ``slow" interfaces, and for both short and (whenever the solution is global) large times, which we expect to be sharp. In the case of weak slippage, we obtain partial results for short times, which include a quantitative bound for moderate growths of the convective term. Our approach is based on energy/entropy methods shaped upon suitable extensions of Stampacchia's Lemma.

Propagation of support in one-dimensional convected thin-film flow / Giacomelli, Lorenzo; A., Shishkov. - In: INDIANA UNIVERSITY MATHEMATICS JOURNAL. - ISSN 0022-2518. - STAMPA. - 54:(2005), pp. 1181-1215. [10.1512/iumj.2005.54.2532]

Propagation of support in one-dimensional convected thin-film flow

GIACOMELLI, Lorenzo;
2005

Abstract

In one space dimension, we study the finite speed of propagation property for zero contact--angle solutions of the thin-film equation in presence of a convective term. In the case of strong slippage, we obtain bounds in terms of the initial mass for both the ``fast" and the ``slow" interfaces, and for both short and (whenever the solution is global) large times, which we expect to be sharp. In the case of weak slippage, we obtain partial results for short times, which include a quantitative bound for moderate growths of the convective term. Our approach is based on energy/entropy methods shaped upon suitable extensions of Stampacchia's Lemma.
2005
Partial Differential Equations; Free Boundary Problems; Thin-Film Equations; Lubrication Theory
01 Pubblicazione su rivista::01a Articolo in rivista
Propagation of support in one-dimensional convected thin-film flow / Giacomelli, Lorenzo; A., Shishkov. - In: INDIANA UNIVERSITY MATHEMATICS JOURNAL. - ISSN 0022-2518. - STAMPA. - 54:(2005), pp. 1181-1215. [10.1512/iumj.2005.54.2532]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/102788
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