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In this paper, we study the relationship between the long time behavior of a solution u(t, x) of the Navier-Stokes system with no external force in R and the asymptotic behavior as |x| → ∞ of its initial value u0. In particular, for initial values u0 small in a certain sense, we show that if the sequence of dilations λnu0(λn·) converges weakly to z(·) as λn… (More)

- R Weber dos Santos, F Dickstein, D Marchesin
- Biomedizinische Technik. Biomedical engineering
- 2002

Recently, B. Roth and M. Woods [7] suggested a reexamination of MCG interpretation through currents transversal to the wave propagation direction. They also gave a formula J'(theta) for the dependence of the current intensity on the angle theta between straight fibers and the plane wave front. Here we study more general situations, including current… (More)

- Rodrigo Weber dos Santos, Flavio Dickstein
- FIMH
- 2003

(1.1) ut −∆u = |u|u, u|∂Ω = 0, u(0) = u0. It is well known that the above initial value problem is locally well-posed. More precisely, there exists a maximal time 0 < Tu0 ≤ ∞ and a (unique) function u ∈ C([0, Tu0), C0(Ω))∩C((0, Tu0), C(Ω))∩C((0, Tu0), C0(Ω)) which is a classical solution of (1.1) on (0, Tu0) and such that u(0) = u0. Furthermore, there… (More)

In this paper we study the Cauchy problem for the semilinear heat and Schrödinger equations, with the nonlinear term f(u) = λ|u|αu. We show that low regularity of f (i.e., α > 0 but small) limits the regularity of any possible solution for a certain class of smooth initial data. We employ two different methods, which yield two different types of results. On… (More)

History matching is an important inverse problem extensively used to estimate petrophysical properties of an oil reservoir by matching a numerical simulation to the reservoir’s history of oil production. In this work, we present a method for the resolution of a history matching problem that aims to estimate the permeability field of a reservoir using the… (More)

- Carolina Ribeiro Xavier, Elisa Portes dos Santos, +4 authors Rodrigo Weber dos Santos
- ICCSA
- 2010

- Thierry Cazenave, Flavio Dickstein, Fred B. Weissler
- SIAM J. Math. Analysis
- 2013

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