Zobrazeno 1 - 10
of 114
pro vyhledávání: '"Giacomelli, Lorenzo"'
We consider the thin-film equation for a class of free boundary conditions modelling friction at the contact line, as introduced by E and Ren. Our analysis focuses on formal long-time asymptotics of solutions in the perfect wetting regime. In particu
Externí odkaz:
http://arxiv.org/abs/2302.03005
In the regime of lubrication approximation, we look at spreading phenomena under the action of singular potentials of the form $P(h)\approx h^{1-m}$ as $h\to 0^+$ with $m>1$, modeling repulsion between the liquid-gas interface and the substrate. We a
Externí odkaz:
http://arxiv.org/abs/2207.00700
Autor:
Palleschi, Simonetta, Silvestroni, Leopoldo, Rossi, Barbara, Dinarelli, Simone, Magi, Marco, Giacomelli, Lorenzo, Bettucci, Andrea
Publikováno v:
In Biosensors and Bioelectronics: X December 2024 21
We study global minimizers of a functional modeling the free energy of thin liquid layers over a solid substrate under the combined effect of surface, gravitational, and intermolecular potentials. When the latter ones have a mild repulsive singularit
Externí odkaz:
http://arxiv.org/abs/2109.06683
Publikováno v:
International Mathematics Research Notices IMRN, 2022
We consider a prototypical nonlinear parabolic equation whose flux has three distinguished features: it is nonlinear with respect to both the unknown and its gradient, it is homogeneous, and it depends only on the direction of the gradient. For such
Externí odkaz:
http://arxiv.org/abs/2102.02587
We consider a cantilever beam which possesses a possibly non-uniform permanent magnetization, and whose shape is controlled by an applied magnetic field. We model the beam as a plane elastic curve and we suppose that the magnetic field acts upon the
Externí odkaz:
http://arxiv.org/abs/2003.02696
Autor:
Giacomelli, Lorenzo, Łasica, Michał
Let $\boldsymbol u$ be the minimizer of vectorial total variation ($VTV$) with $L^2$ data-fidelity term on an interval $I$. We show that the total variation of $\boldsymbol u$ over any subinterval of $I$ is bounded by that of the datum over the same
Externí odkaz:
http://arxiv.org/abs/1806.02456
We consider the 1-harmonic flow of maps from a bounded domain into a submanifold of a Euclidean space, i.e. the gradient flow of the total variation functional restricted to maps taking values in the manifold. We restrict ourselves to Lipschitz initi
Externí odkaz:
http://arxiv.org/abs/1711.07460
Publikováno v:
Adv. Calc. Var., 11 (2018), 405-432
We consider the partial differential equation $$ u-f={\rm div}\left(u^m\frac{\nabla u}{|\nabla u|}\right) $$ with $f$ nonnegative and bounded and $m\in\mathbb{R}$. We prove existence and uniqueness of solutions for both the Dirichlet problem (with bo
Externí odkaz:
http://arxiv.org/abs/1702.03746
Publikováno v:
Comm. Partial Differential Equations, 42 (4), (2017) 556-578
We consider the Cauchy problem for two prototypes of flux-saturated diffusion equations. In arbitrary space dimension, we give an optimal condition on the growth of the initial datum which discriminates between occurrence or nonoccurrence of a waitin
Externí odkaz:
http://arxiv.org/abs/1607.01245