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math.NA2025
Non-self-adjoint sixth-order eigenvalue problems arising from clamped elastic thin films on closed domains
N C Papanicolaou, I C Christov
Sixth-order boundary value problems (BVPs) arise in thin-film flows with a surface that has elastic bending resistance. We consider the case in which the elastic interface is clamp…
math.NA2024★ 7 cited
Sixth-order parabolic equation on an interval: Eigenfunction expansion, Green's function, and intermediate asymptotics for a finite thin film with elastic resistance
Nectarios C. Papanicolaou, Ivan C. Christov
A linear sixth-order partial differential equation (PDE) of ``parabolic'' type describes the dynamics of thin liquid films beneath surfaces with elastic bending resistance when def…
math.NA2023★ 4 cited
Orthonormal eigenfunction expansions for sixth-order boundary value problems
N C Papanicolaou, I C Christov
Sixth-order boundary value problems (BVPs) arise in thin-film flows with a surface that has elastic bending resistance. To solve such problems, we first derive a complete set of od…