caa a22 4500 605515980 CHVBK 20210128100712.0 cr unu---uuuuu 210128e20151101xx s 000 0 eng 10.1007/s00205-015-0882-x doi (NATIONALLICENCE)springer-10.1007/s00205-015-0882-x Knüpfer Hans University of Heidelberg, Im Neuenheimer Feld 294, Heidelberg, Germany aut Well-Posedness for a Class of Thin-Film Equations with General Mobility in the Regime of Partial Wetting [Elektronische Daten] [Hans Knüpfer] 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. Springer-Verlag Berlin Heidelberg, 2015 Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 218/2(2015-11-01), 1083-1130 0003-9527 218:2<1083 2015 218 205 https://doi.org/10.1007/s00205-015-0882-x text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00205-015-0882-x text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Knüpfer Hans University of Heidelberg, Im Neuenheimer Feld 294, Heidelberg, Germany aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 218/2(2015-11-01), 1083-1130 0003-9527 218:2<1083 2015 218 205