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Finite-time singularity versus global regularity for hyper-viscous Hamilton-Jacobi-like equations
(Institute of Physics, 2003)
The global regularity for the two- and three-dimensional Kuramoto-Sivashinsky equations is one of the major open questions in nonlinear analysis. Inspired by this question, we introduce in this paper and family of hyper-viscous ...
Existence of a Solution to the Line Contact Problem of Elastohydrodynamic Lubrication
(Cambridge University Press, 2003-06)
We prove the existence of a solution to a free boundary value problem arising in elastohydrodynamic lubrication. Previously, the existence was proved only under severe restrictions on the range of the physical parameters. ...