Well-Posedness for a Class of Thin-Film Equations with General Mobility in the Regime of Partial Wetting
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| 024 | 7 | 0 | |a 10.1007/s00205-015-0882-x |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00205-015-0882-x | ||
| 100 | 1 | |a Knüpfer |D Hans |u University of Heidelberg, Im Neuenheimer Feld 294, Heidelberg, Germany |4 aut | |
| 245 | 1 | 0 | |a Well-Posedness for a Class of Thin-Film Equations with General Mobility in the Regime of Partial Wetting |h [Elektronische Daten] |c [Hans Knüpfer] |
| 520 | 3 | |a We establish well-posedness for the family of thin-film equations 1 $$\left \{\begin{array}{ll}h_t + (h^n h_{xxx})_x \ = \ 0 \quad \ {\rm in } \ \{ h > 0 \},\\ h \ = \ 0, \ |h_x| \ = \ 1 \quad\quad {\rm on } \ \partial \{ h > 0 \}\end{array}\right. $$ h t + ( h n h x x x ) x = 0 in { h > 0 } , h = 0 , | h x | = 1 on ∂ { h > 0 } with $${n \in (0,\frac {14}{5}) \backslash \{ 1, 2 \}}$$ n ∈ ( 0 , 14 5 ) \ { 1 , 2 } . The model (1) with $${n \in (0,3]}$$ n ∈ ( 0 , 3 ] has been used to describe the evolution of a capillary driven thin liquid droplet on a solid substrate in terms of its height profile $${h \geqq 0}$$ h ≧ 0 . The family of thin-film equations (1) provides a model problem to investigate contact line propagation in fluid dynamics under relaxed slip conditions. The parabolicity of the fourth order parabolic problem degenerates at the free boundary, which leads to a loss of regularity at the moving contact point. Our solutions are regular in terms of the two variables d(x) and d(x)3−n , where d(x) is the distance to the free boundary. The main technical difficulty in the analysis of (1) is related to the loss of regularity at the contact points. | |
| 540 | |a Springer-Verlag Berlin Heidelberg, 2015 | ||
| 773 | 0 | |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 218/2(2015-11-01), 1083-1130 |x 0003-9527 |q 218:2<1083 |1 2015 |2 218 |o 205 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00205-015-0882-x |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00205-015-0882-x |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Knüpfer |D Hans |u University of Heidelberg, Im Neuenheimer Feld 294, Heidelberg, Germany |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 218/2(2015-11-01), 1083-1130 |x 0003-9527 |q 218:2<1083 |1 2015 |2 218 |o 205 | ||