Zobrazeno 1 - 10
of 135
pro vyhledávání: '"Bonforte, Matteo"'
We consider a diffused interface version of the volume-preserving mean curvature flow in the Euclidean space, and prove, in every dimension and under natural assumptions on the initial datum, exponential convergence towards single "diffused balls".
Externí odkaz:
http://arxiv.org/abs/2407.18868
We study nonnegative solutions to the Cauchy problem for the Fractional Fast Diffusion Equation on a suitable class of connected, noncompact Riemannian manifolds. This parabolic equation is both singular and nonlocal: the diffusion is driven by the (
Externí odkaz:
http://arxiv.org/abs/2405.17126
Our focus is on the fast diffusion equation $\partial_t u=\Delta_p u$ with $p<2$ in the whole Euclidean space of dimension $N\geq 2$. The properties of the solutions to the $p$-Laplace Cauchy problem change in several special values of the parameter
Externí odkaz:
http://arxiv.org/abs/2405.05405
Autor:
Bonforte, Matteo, Salort, Ariel
We study regularity properties of solutions to nonlinear and nonlocal evolution problems driven by the so-called \emph{$0$-order fractional $p-$Laplacian} type operators: $$ \partial_t u(x,t)=\mathcal{J}_p u(x,t):=\int_{\mathbb{R}^n} J(x-y)|u(y,t)-u(
Externí odkaz:
http://arxiv.org/abs/2404.00479
We consider a class of porous medium type of equations with Caputo time derivative. The prototype problem reads as $\Dc u=-\A u^m$ and is posed on a bounded Euclidean domain $\Omega\subset\mathbb{R}^N$ with zero Dirichlet boundary conditions. The ope
Externí odkaz:
http://arxiv.org/abs/2401.03234
Autor:
Bonforte, Matteo, Figalli, Alessio
The Fast Diffusion Equation (FDE) $u_t= \Delta u^m$, with $m\in (0,1)$, is an important model for singular nonlinear (density dependent) diffusive phenomena. Here, we focus on the Cauchy-Dirichlet problem posed on smooth bounded Euclidean domains. In
Externí odkaz:
http://arxiv.org/abs/2308.08394
Autor:
Bonforte, Matteo, Endal, Jørgen
Publikováno v:
J. Funct. Anal., 284(6):109831, 2023
We establish boundedness estimates for solutions of generalized porous medium equations of the form $$ \partial_t u+(-\mathfrak{L})[u^m]=0\quad\quad\text{in $\mathbb{R}^N\times(0,T)$}, $$ where $m\geq1$ and $-\mathfrak{L}$ is a linear, symmetric, and
Externí odkaz:
http://arxiv.org/abs/2205.06850
We study the homogeneous Cauchy-Dirichlet Problem (CDP) for a nonlinear and nonlocal diffusion equation of singular type of the form $\partial_t u =-\mathcal{L} u^m$ posed on a bounded Euclidean domain $\Omega\subset\mathbb{R}^N$ with smooth boundary
Externí odkaz:
http://arxiv.org/abs/2203.12545
We provide a scheme of a recent stability result for a family of Gagliardo-Nirenberg-Sobolev (GNS) inequalities, which is equivalent to an improved entropy - entropy production inequality associated with an appropriate fast diffusion equation (FDE) w
Externí odkaz:
http://arxiv.org/abs/2202.09693