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pro vyhledávání: '"Segatti, Antonio"'
In this paper, we discuss existence and finite speed of propagation for the solutions to an initial-boundary value problem for a family of fractional thin-film equations in a bounded domain in $\mathbb{R}^d$. The nonlocal operator we consider is the
Externí odkaz:
http://arxiv.org/abs/2404.03633
Autor:
Canevari, Giacomo, Segatti, Antonio
In this paper we discuss the behavior of the Oseen-Frank model for nematic liquid crystals in the limit of vanishing thickness. More precisely, in a thin slab~$\Omega\times (0,h)$ with~$\Omega\subset \mathbb{R}^2$ and $h>0$ we consider the one-consta
Externí odkaz:
http://arxiv.org/abs/2307.11396
Autor:
Canevari, Giacomo, Segatti, Antonio
We consider the gradient flow of a Ginzburg-Landau functional of the type \[ F_\varepsilon^{\mathrm{extr}}(u):=\frac{1}{2}\int_M \left|D u\right|_g^2 + \left|\mathscr{S} u\right|^2_g +\frac{1}{2\varepsilon^2}\left(\left|u\right|^2_g-1\right)^2\mathrm
Externí odkaz:
http://arxiv.org/abs/2112.15080
We introduce a heat flow associated to half-harmonic maps, which have been introduced by Da Lio and Rivi\`ere. Those maps exhibit integrability by compensation in one space dimension and are related to harmonic maps with free boundary. We consider a
Externí odkaz:
http://arxiv.org/abs/2111.14171
Autor:
Canevari, Giacomo, Segatti, Antonio
In this paper we consider the gradient flow of the following Ginzburg-Landau type energy \[ F_\varepsilon(u) := \frac{1}{2}\int_{M}\vert D u\vert_g^2 +\frac{1}{2\varepsilon^2}\left(\vert u\vert_g^2-1\right)^2\mathrm{vol}_g. \] This energy is defined
Externí odkaz:
http://arxiv.org/abs/2108.01321
Autor:
Canevari, Giacomo, Segatti, Antonio
Publikováno v:
In Journal of Functional Analysis 1 December 2023 285(11)
Autor:
Segatti, Antonio, Vázquez, Juan Luis
This paper deals with a nonlinear degenerate parabolic equation of order $\alpha$ between 2 and 4 which is a kind of fractional version of the Thin Film Equation. Actually, this one corresponds to the limit value $\alpha=4$ while the Porous Medium Eq
Externí odkaz:
http://arxiv.org/abs/1902.01264
This paper develops the so-called Weighted Energy-Dissipation (WED) variational approach for the analysis of gradient flows in metric spaces. This focuses on the minimization of the parameter-dependent global-in-time functional of trajectories \[ \ma
Externí odkaz:
http://arxiv.org/abs/1801.04988
This paper deals with the Cauchy-Dirichlet problem for the fractional Cahn-Hilliard equation. The main results consist of global (in time) existence of weak solutions, characterization of parabolic smoothing effects (implying under proper condition e
Externí odkaz:
http://arxiv.org/abs/1801.01722
Autor:
Hrkac, Gino, Pfeiler, Carl-Martin, Praetorius, Dirk, Ruggeri, Michele, Segatti, Antonio, Stiftner, Bernhard
Publikováno v:
Advances in Computational Mathematics, 45 (2019), 1329-1368
We consider the numerical approximation of the Landau-Lifshitz-Gilbert equation, which describes the dynamics of the magnetization in ferromagnetic materials. In addition to the classical micromagnetic contributions, the energy comprises the Dzyalosh
Externí odkaz:
http://arxiv.org/abs/1712.03795