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8 papers · 2 filters
The Navier-slip thin-film equation for 3D fluid films: existence and uniqueness
Manuel V. Gnann, Mircea Petrache
We consider the thin-film equation in physical space dimensions (i.e., one dimension in time and two lateral dimens…
Existence and nonexistence of positive solutions to some fully nonlinear equation in one dimension
Patricio Felmer, Norihisa Ikoma
In this paper, we consider the existence (and nonexistence) of solutions to \[ -\mathcal{M}_{λ,Λ}^\pm (u'') + V(x) u = f(u) \quad {\rm in} \ \mathbf{R} \] where $\mathcal{M}_{λ,Λ}^…
Scattering in the energy space for Boussinesq equations
Claudio Muñoz, Felipe Poblete, Juan C. Pozo
In this note we show that all small solutions in the energy space of the generalized 1D Boussinesq equation must decay to zero as time tends to infinity, strongly on slightly prope…
Symmetry breaking and restoration in the Ginzburg-Landau model of nematic liquid crystals
Marcel Clerc, Michał Kowalczyk, Panayotis Smyrnelis
In this paper we study qualitative properties of global minimizers of the Ginzburg-Landau energy which describes light-matter interaction in the theory of nematic liquid crystals n…
Periodic solutions to the Cahn-Hilliard equation in the plane
Andrea Malchiodi, Rainer Mandel, Matteo Rizzi
In this paper we construct entire solutions to the Cahn-Hilliard equation in the Euclidean plane, where is the standard double-we…
Ancient shrinking spherical interfaces in the Allen-Cahn flow
Manuel del Pino, Konstantinos T. Gkikas
We consider the parabolic Allen-Cahn equation in , , We construct an ancient radial…