Zobrazeno 1 - 10
of 82
pro vyhledávání: '"Endal, Jørgen"'
We study the spatially homogeneous granular medium equation \[\partial_t\mu=\rm{div}(\mu\nabla V)+\rm{div}(\mu(\nabla W \ast \mu))+\Delta\mu\,,\] within a large and natural class of the confinement potentials $V$ and interaction potentials $W$. The c
Externí odkaz:
http://arxiv.org/abs/2405.18034
We study well-posedness of degenerate mixed-type parabolic-hyperbolic equations $$\partial_t u+\mathrm{div}\big(f(u)\big)=\mathcal{L}[b(u)]$$on bounded domains with general Dirichlet boundary/exterior conditions. The nonlocal diffusion operator $\mat
Externí odkaz:
http://arxiv.org/abs/2310.06453
We study the existence and uniqueness of source-type solutions to the Cauchy problem for the heat equation with fast convection under certain tail control assumptions. We allow the solutions to change sign, but we will in fact show that they have the
Externí odkaz:
http://arxiv.org/abs/2303.01908
Publikováno v:
Calc. Var., 62:136, 2023
We consider the evolution problem associated to the infinity fractional Laplacian introduced by Bjorland, Caffarelli and Figalli (2012) as the infinitesimal generator of a non-Brownian tug-of-war game. We first construct a class of viscosity solution
Externí odkaz:
http://arxiv.org/abs/2210.06414
We study the large-time behaviour of nonnegative solutions to the Cauchy problem for a nonlocal heat equation with a nonlinear convection term. The diffusion operator is the infinitesimal generator of a stable L\'evy process, which may be highly anis
Externí odkaz:
http://arxiv.org/abs/2207.01874
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
Publikováno v:
Discrete Contin. Dyn. Syst., 43(3&4):1319-1346, 2023
We obtain new equitightness and $C([0,T];L^p(\mathbb{R}^N))$-convergence results for finite-difference approximations of generalized porous medium equations of the form $$ \partial_tu-\mathfrak{L}[\varphi(u)]=g\qquad\text{in $\mathbb{R}^N\times(0,T)$
Externí odkaz:
http://arxiv.org/abs/2202.02297
Publikováno v:
In Journal de mathématiques pures et appliquées August 2024 188:26-72
Publikováno v:
Asymptot. Anal., 127(3):201--216, 2022
We propose two asymptotic expansions of two interrelated integral-type averages, in the context of the fractional $\infty$-Laplacian $\Delta_\infty^s$ for $s\in (\frac{1}{2},1)$. This operator has been introduced and first studied in [Bjorland, C., C
Externí odkaz:
http://arxiv.org/abs/2007.15765
The classical Stefan problem is one of the most studied free boundary problems of evolution type. Recently, there has been interest in treating the corresponding free boundary problem with nonlocal diffusion. We start the paper by reviewing the main
Externí odkaz:
http://arxiv.org/abs/2002.01386