Zobrazeno 1 - 10
of 20
pro vyhledávání: '"Bruno Volzone"'
Autor:
Roberta Volpicelli, Bruno Volzone
Publikováno v:
Le Matematiche, Vol 62, Iss 1, Pp 135-156 (2007)
We consider the solution u of the Cauchy-Dirichlet problem for a class of linear parabolic equations in which the coefficient of the zero order term could have a singularity at the origin of the type 1/|x|^2 . We prove that u can be compared “in th
Externí odkaz:
https://doaj.org/article/3b378bcf00e54d629009408cecd0de56
Publikováno v:
Inventiones mathematicae. 218:889-977
We analyze under which conditions equilibration between two competing effects, repulsion modeled by nonlinear diffusion and attraction modeled by nonlocal interaction, occurs. This balance leads to continuous compactly supported radially decreasing e
We study an anisotropic, possibly non-homogeneous version of the evolution $p$-Laplacian equation when fast diffusion holds in all directions. We develop the basic theory and prove symmetrization results from which we derive $L^1$ to $L^\infty$ estim
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::167c4230bccc466e52b453f7be94e594
Autor:
Bruno Volzone, Lorenzo Brasco
We study the long-time behavior for the solution of the Porous Medium Equation in an open bounded connected set, with smooth boundary. Homogeneous Dirichlet boundary conditions are considered. We prove that if the initial datum has sufficiently small
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a40779df3ca490301163f5dda245a878
http://arxiv.org/abs/2011.04619
http://arxiv.org/abs/2011.04619
Autor:
Bruno Volzone, Vincenzo Ferone
We provide new direct methods to establish symmetrization results in the form of a mass concentration (that is, integral) comparison for fractional elliptic equations of the type $$(-\Delta )^{s}u=f \, (0
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f1b778c30a315ddaa743855a6a26c589
http://arxiv.org/abs/2007.13195
http://arxiv.org/abs/2007.13195
We prove the existence of self-similar fundamental solutions (SSF) of the anisotropic porous medium equation in the suitable fast diffusion range. Each of such SSF solutions is uniquely determined by its mass. We also obtain the asymptotic behaviour
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2eb363528a832efbfee2c5afee9c5350
http://arxiv.org/abs/2007.00122
http://arxiv.org/abs/2007.00122
Publikováno v:
Calculus of Variations and Partial Differential Equations, 59 (6)
Chan, H, González, M D M, Huang, Y, Mainini, E & Volzone, B 2020, ' Uniqueness of entire ground states for the fractional plasma problem ', Calculus of Variations and Partial Differential Equations, vol. 59, no. 195 . https://doi.org/10.1007/s00526-020-01845-y
Chan, H, González, M D M, Huang, Y, Mainini, E & Volzone, B 2020, ' Uniqueness of entire ground states for the fractional plasma problem ', Calculus of Variations and Partial Differential Equations, vol. 59, no. 195 . https://doi.org/10.1007/s00526-020-01845-y
We establish uniqueness of vanishing radially decreasing entire solutions, which we call ground states, to some semilinear fractional elliptic equations. In particular, we treat the fractional plasma equation and the supercritical power nonlinearity.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4544b459e79c98c84e17306131aa062d
https://hdl.handle.net/11567/1028573
https://hdl.handle.net/11567/1028573
Publikováno v:
Feo, F, Huang, Y & Volzone, B 2019, ' Long-time asymptotics for a 1D nonlocal porous medium equation with absorption or convection ', Communications in Contemporary Mathematics . https://doi.org/10.1142/S0219199719500159
In this paper, the long-time asymptotic behaviors of one-dimensional porous medium equations with a fractional pressure and absorption or convection are studied. In the parameter regimes when the nonlocal diffusion is dominant, the entropy method is
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ee288d7fdbfe05179c651d4c1978e3e3
http://hdl.handle.net/11367/72311
http://hdl.handle.net/11367/72311
Autor:
Bruno Volzone, Juan Luis Vázquez
Publikováno v:
Journal de Mathématiques Pures et Appliquées. 103:535-556
We obtain a priori estimates with best constants for the solutions of the fractional fast diffusion equation u t + ( − Δ ) σ / 2 u m = 0 , posed in the whole space with 0 σ 2 , 0 m ≤ 1 . The estimates are expressed in terms of convenient norms
Publikováno v:
Calculus of Variations and Partial Differential Equations
We consider macroscopic descriptions of particles where repulsion is modelled by non-linear power-law diffusion and attraction by a homogeneous singular kernel leading to variants of the Keller–Segel model of chemotaxis. We analyse the regime in wh
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b4c4f85218215d26f2359fee767a073f
http://arxiv.org/abs/1705.03519
http://arxiv.org/abs/1705.03519