Well-posedness for the Navier Slip Thin-Film equation in the case of partial wetting

2011 ◽  
Vol 64 (9) ◽  
pp. 1263-1296 ◽  
Author(s):  
Hans Knüpfer
Keyword(s):  
Thin Film ◽  
Well Posedness ◽  
Navier Slip ◽  
Partial Wetting ◽  
Thin Film Equation

scholarly journals Well-posedness for the Navier-slip thin-film equation in the case of complete wetting

2014 ◽  
Vol 257 (1) ◽  
pp. 15-81 ◽  
Author(s):  
Lorenzo Giacomelli ◽  
Manuel V. Gnann ◽  
Hans Knüpfer ◽  
Felix Otto
Keyword(s):  
Thin Film ◽  
Well Posedness ◽  
Complete Wetting ◽  
Navier Slip ◽  
Thin Film Equation

scholarly journals Optimal Control for the Thin Film Equation: Convergence of a Multi-Parameter Approach to Track State Constraints Avoiding Degeneracies

2016 ◽  
Vol 16 (4) ◽  
pp. 685-702
Author(s):  
Markus Klein ◽  
Andreas Prohl
Keyword(s):  
Thin Film ◽  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
State Constraints ◽  
Necessary Optimality Conditions ◽  
State Constraint ◽  
The State ◽  
Well Posedness ◽  
Thin Film Equation

AbstractWe consider an optimal control problem subject to the thin-film equation. The PDE constraint lacks well-posedness for general right-hand sides due to possible degeneracies; state constraints are used to circumvent this problematic issue and to ensure well-posedness. Necessary optimality conditions for the optimal control problem are then derived. A convergent multi-parameter regularization is considered which addresses both, the possibly degenerate term in the equation and the state constraint. Some computational studies are then reported which evidence the relevant role of the state constraint, and motivate proper scalings of involved regularization and numerical parameters.

Sign in / Sign up

Export Citation Format

Share Document