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Well-posedness of a system of transport and diffusion equations in space of measures
(Academic Press Inc Elsevier Science, 2020-12)
In this paper, we establish the well-posedness of the following system of two transport equations coupled with a diffusion equation: ∂tμt1+∇⋅(v1[μt]μt1)=N1(t,μt),∂tμt2−Δμt2=N2(t,μt),∂tμt3+∇⋅(v2[μt]μt3)=N3(t,μt), in Rd where ...
A priori bounds and existence of solutions for some nonlocal elliptic problems
(Universidad Autónoma de Madrid, 2018-03)
In this paper we show existence of solutions for some elliptic problems with nonlocal diffusion by means of nonvariational tools. Our proof is based on the use of topological degree, which requires a priori bounds for the ...
Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data: The subcritical case
(IOS Press, 2015-10)
In this paper we continue our study of the large time behavior of the bounded solution to the nonlocal diffusion equation with absorption ut=Lu−upin RN×(0,∞),u(x,0)=u0(x)in RN, where p>1, u0⩾0 and bounded and Lu(x,t)=∫J( ...
A liouville theorem for indefinite fractional diffusion equations and its application to existence of solutions
(American Institute of Mathematical Sciences, 2017-11)
In this work we obtain a Liouville theorem for positive, bounded solutions of the equation where (-δ)s stands for the fractional Laplacian with s 2 (0; 1), and the functions h and f are nondecreasing. The main feature is ...
Anomalous diffusion: Exact solution of the generalized Langevin equation for harmonically bounded particle
(American Physical Society, 2006-01)
We study the effect of a disordered or fractal environment in the irreversible dynamics of a harmonic oscillator. Starting from a generalized Langevin equation and using Laplace analysis, we derive exact expressions for ...
Asymptotic behavior for a nonlocal diffusion equation with absorption and nonintegrable initial data
(American Mathematical Society, 2011-04)
In this paper we study the asymptotic behavior as time goes to infinity of the solution to a nonlocal diffusion equation with absorption modeled by a powerlike reaction -up, p > 1 and set in ℝN. We consider a bounded, ...
The influence of grain size on the hydrogen diffusion in bcc Fe
(Elsevier, 2021-02-15)
This work studies the diffusion of Hydrogen (H) in bcc Fe, containing a high-angle symmetric tilt grain boundary (GB), as a function of both the temperature and the average grain size. For this purpose, we propose a ...
Boundary fluxes for nonlocal diffusion
(Academic Press Inc Elsevier Science, 2007-12)
We study a nonlocal diffusion operator in a bounded smooth domain prescribing the flux through the boundary. This problem may be seen as a generalization of the usual Neumann problem for the heat equation. First, we prove ...