Recent progress in the theory of nonlinear diffusion with fractional Laplacian operators
JL Vázquez - arXiv preprint arXiv:1401.3640, 2014 - arxiv.org
We report on recent progress in the study of nonlinear diffusion equations involving
nonlocal, long-range diffusion effects. Our main concern is the so-called fractional porous …
nonlocal, long-range diffusion effects. Our main concern is the so-called fractional porous …
[图书][B] Nonlocal diffusion and applications
C Bucur, E Valdinoci - 2016 - Springer
The purpose of these pages is to collect a set of notes that are a result of several talks and
minicourses delivered here and there in the world (Milan, Cortona, Pisa, Roma, Santiago del …
minicourses delivered here and there in the world (Milan, Cortona, Pisa, Roma, Santiago del …
Hitchhikerʼs guide to the fractional Sobolev spaces
E Di Nezza, G Palatucci, E Valdinoci - Bulletin des sciences …, 2012 - Elsevier
This paper deals with the fractional Sobolev spaces Ws, p. We analyze the relations among
some of their possible definitions and their role in the trace theory. We prove continuous and …
some of their possible definitions and their role in the trace theory. We prove continuous and …
The mathematical theories of diffusion: nonlinear and fractional diffusion
We describe the mathematical theory of diffusion and heat transport with a view to including
some of the main directions of recent research. The linear heat equation is the basic …
some of the main directions of recent research. The linear heat equation is the basic …
Nonlinear porous medium flow with fractional potential pressure
LA Caffarelli, JL Vazquez - arXiv preprint arXiv:1001.0410, 2010 - arxiv.org
We study a porous medium equation, with nonlocal diffusion effects given by an inverse
fractional Laplacian operator. We pose the problem in n-dimensional space for all t> 0 with …
fractional Laplacian operator. We pose the problem in n-dimensional space for all t> 0 with …
A general fractional porous medium equation
A De Pablo, F Quirós, A Rodríguez… - … on Pure and Applied …, 2012 - Wiley Online Library
We develop a theory of existence and uniqueness for the following porous medium equation
with fractional diffusion:\input amssym\left {∂ u ∂ t+\left (‐Δ\right)^ σ/2\left (\left| u\right|^ m‐1 …
with fractional diffusion:\input amssym\left {∂ u ∂ t+\left (‐Δ\right)^ σ/2\left (\left| u\right|^ m‐1 …
Nonlinear diffusion with fractional Laplacian operators
JL Vázquez - Nonlinear partial differential equations: the Abel …, 2012 - Springer
We describe two models of flow in porous media including nonlocal (long-range) diffusion
effects. The first model is based on Darcy's law and the pressure is related to the density by …
effects. The first model is based on Darcy's law and the pressure is related to the density by …
Regularity of solutions of the fractional porous medium flow
We study a porous medium equation with nonlocal diffusion effects given by an inverse
fractional Laplacian operator. The precise model is ut=∇·(u∇(−)− su), 0< s< 1. The problem …
fractional Laplacian operator. The precise model is ut=∇·(u∇(−)− su), 0< s< 1. The problem …
[HTML][HTML] Quantitative local and global a priori estimates for fractional nonlinear diffusion equations
M Bonforte, JL Vázquez - Advances in Mathematics, 2014 - Elsevier
We establish quantitative estimates for solutions u (t, x) to the fractional nonlinear diffusion
equation,∂ t u+(− Δ) s (um)= 0 in the whole range of exponents m> 0, 0< s< 1. The equation …
equation,∂ t u+(− Δ) s (um)= 0 in the whole range of exponents m> 0, 0< s< 1. The equation …
The nonlocal porous medium equation: Barenblatt profiles and other weak solutions
A degenerate nonlinear nonlocal evolution equation is considered; it can be understood as
a porous medium equation whose pressure law is nonlinear and nonlocal. We show the …
a porous medium equation whose pressure law is nonlinear and nonlocal. We show the …