Continuity of the dynamics in a localized large diffusion problem with nonlinear boundary conditions

This paper is concerned with singular perturbations in parabolic problems subjected to nonlinear Neumann boundary conditions. We consider the case for which the diffusion coefficient blows up in a subregion Omega(0) which is interior to the physical domain Omega subset of R(n). We prove, under natural assumptions, that the associated attractors behave continuously as the diffusion coefficient blows up locally uniformly in Omega(0) and converges uniformly to a continuous and positive function in Omega(1) = (Omega) over bar\Omega(0). (C) 2009 Elsevier Inc. All rights reserved.

Dynamics in dumbbell domains II. The limiting problem

In this work we continue the analysis of the asymptotic dynamics of reaction-diffusion problems in a dumbbell domain started in [J.M. Arrieta, AN Carvalho, G. Lozada-Cruz, Dynamics in dumbbell domains I. Continuity of the set of equilibria, J. Differential Equations 231 (2) (2006) 551-597]. Here we study the limiting problem, that is, an evolution problem in a ""domain"" which consists of an open, bounded and smooth set Omega subset of R(N) with a curve R(0) attached to it. The evolution in both parts of the domain is governed by a parabolic equation. In Omega the evolution is independent of the evolution in R(0) whereas in R(0) the evolution depends on the evolution in Omega through the continuity condition of the solution at the junction points. We analyze in detail the linear elliptic and parabolic problem, the generation of linear and nonlinear semigroups, the existence and structure of attractors. (C) 2009 Elsevier Inc. All rights reserved.

Dynamics in dumbbell domains III. Continuity of attractors

In this paper we conclude the analysis started in [J.M. Arrieta, AN Carvalho, G. Lozada-Cruz, Dynamics in dumbbell domains I. Continuity of the set of equilibria, J. Differential Equations 231 (2006) 551-597] and continued in [J.M. Arrieta, AN Carvalho, G. Lozada-Cruz, Dynamics in dumbbell domains II. The limiting problem, J. Differential Equations 247 (1) (2009) 174-202 (this issue)] concerning the behavior of the asymptotic dynamics of a dissipative reaction-diffusion equation in a dumbbell domain as the channel shrinks to a line segment. In [J.M. Arrieta, AN Carvalho. G. Lozada-Cruz, Dynamics in dumbbell domains I. Continuity of the set of equilibria, J. Differential Equations 231 (2006) 551-597], we have established an appropriate functional analytic framework to address this problem and we have shown the continuity of the set of equilibria. In [J.M. Arrieta, AN Carvalho, G. Lozada-Cruz. Dynamics in dumbbell domains II. The limiting problem, J. Differential Equations 247 (1) (2009) 174-202 (this issue)], we have analyzed the behavior of the limiting problem. In this paper we show that the attractors are Upper semicontinuous and, moreover, if all equilibria of the limiting problem are hyperbolic, then they are lower semicontinuous and therefore, continuous. The continuity is obtained in L(p) and H(1) norms. (C) 2008 Elsevier Inc. All rights reserved.

Global solutions for impulsive abstract partial differential equations

In this paper, we study the existence of global solutions for a class of impulsive abstract functional differential equation. An application involving a parabolic system With impulses is considered. (c) 2008 Elsevier Ltd. All rights reserved.

Strongly damped wave problems: Bootstrapping and regularity of solutions

The aim of the article is to present a unified approach to the existence, uniqueness and regularity of solutions to problems belonging to a class of second order in time semilinear partial differential equations in Banach spaces. Our results are applied next to a number of examples appearing in literature, which fall into the class of strongly damped semilinear wave equations. The present work essentially extends the results on the existence and regularity of solutions to such problems. Previously, these problems have been considered mostly within the Hilbert space setting and with the main part operators being selfadjoint. In this article we present a more general approach, involving sectorial operators in reflexive Banach spaces. (C) 2008 Elsevier Inc. All rights reserved.

Non-autonomous semilinear evolution equations with almost sectorial operators

Inspired by the theory of semigroups of growth a, we construct an evolution process of growth alpha. The abstract theory is applied to study semilinear singular non-autonomous parabolic problems. We prove that. under natural assumptions. a reasonable concept of solution can be given to Such semilinear singularly non-autonomous problems. Applications are considered to non-autonomous parabolic problems in space of Holder continuous functions and to a parabolic problem in a domain Omega subset of R(n) with a one dimensional handle.

Aerosol inorganic composition at a tropical site: Discrepancies between filter-based sampling and a semi-continuous method

The concentrations of the water-soluble inorganic aerosol species, ammonium (NH4+), nitrate (NO3-), chloride (Cl-), and sulfate (SO42-), were measured from September to November 2002 at a pasture site in the Amazon Basin (Rondnia, Brazil) (LBA-SMOCC). Measurements were conducted using a semi-continuous technique (Wet-annular denuder/Steam-Jet Aerosol Collector: WAD/SJAC) and three integrating filter-based methods, namely (1) a denuder-filter pack (DFP: Teflon and impregnated Whatman filters), (2) a stacked-filter unit (SFU: polycarbonate filters), and (3) a High Volume dichotomous sampler (HiVol: quartz fiber filters). Measurements covered the late dry season (biomass burning), a transition period, and the onset of the wet season (clean conditions). Analyses of the particles collected on filters were performed using ion chromatography (IC) and Particle-Induced X-ray Emission spectrometry (PIXE). Season-dependent discrepancies were observed between the WAD/SJAC system and the filter-based samplers. During the dry season, when PM2.5 (D-p <= 2.5 mu m) concentrations were similar to 100 mu g m(-3), aerosol NH4+ and SO42- measured by the filter-based samplers were on average two times higher than those determined by the WAD/SJAC. Concentrations of aerosol NO3- and Cl- measured with the HiVol during daytime, and with the DFP during day- and nighttime also exceeded those of the WAD/SJAC by a factor of two. In contrast, aerosol NO3- and Cl- measured with the SFU during the dry season were nearly two times lower than those measured by the WAD/SJAC. These differences declined markedly during the transition period and towards the cleaner conditions during the onset of the wet season (PM2.5 similar to 5 mu g m(-3)); when filter-based samplers measured on average 40-90% less than the WAD/SJAC. The differences were not due to consistent systematic biases of the analytical techniques, but were apparently a result of prevailing environmental conditions and different sampling procedures. For the transition period and wet season, the significance of our results is reduced by a low number of data points. We argue that the observed differences are mainly attributable to (a) positive and negative filter sampling artifacts, (b) presence of organic compounds and organosulfates on filter substrates, and (c) a SJAC sampling efficiency of less than 100%.

A general Trotter-Kato formula for a class of evolution operators

In this article we prove new results concerning the existence and various properties of an evolution system U(A+B)(t, s)0 <= s <= t <= T generated by the sum -(A(t) + B(t)) of two linear, time-dependent, and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing L(B) for the algebra of all linear bounded operators on B, we can express U(A+B)(t, s)0 <= s <= t <= T as the strong limit in C(8) of a product of the holomorphic contraction semigroups generated by -A (t) and - B(t), respectively, thereby proving a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t) + B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND(t is an element of)[0,T] D(A(t) + B(t)) everywhere dense in B. We obtain a special case of our formula when B(t) = 0, which, in effect, allows us to reconstruct U(A)(t, s)0 <=(s)<=(t)<=(T) very simply in terms of the semigroup generated by -A(t). We then illustrate our results by considering various examples of nonautonomous parabolic initial-boundary value problems, including one related to the theory of timedependent singular perturbations of self-adjoint operators. We finally mention what we think remains an open problem for the corresponding equations of Schrodinger type in quantum mechanics.

A Trotter-Kato product formula for a class of non-autonomous evolution equations

In this article dedicated to Professor V. Lakshmikantham on the occasion of the celebration of his 84th birthday, we announce new results concerning the existence and various properties of an evolution system UA+B(t, s)(0 <= s <= t <= T) generated by the sum -(A(t)+B(t)) of two linear, time-dependent and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing G(B) for the algebra of all linear bounded operators on B, we can express UA+B(t, s)(0 <= s <= t <= T) as the strong limit in L(B) of a product of the holomorphic contraction semigroups generated by -A(t) and -B(t), thereby getting a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t)+B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND D-t epsilon[0,D-T](A(t)+B(t)) everywhere dense in B. We then mention several possible applications of our product formula to various classes of non-autonomous parabolic initial-boundary value problems, as well as to evolution problems of Schrodinger type related to the theory of time-dependent singular perturbations of self-adjoint operators in quantum mechanics. We defer all the proofs and all the details of the applications to a separate publication. (C) 2008 Elsevier Ltd. All rights reserved.

Microgranitic Enclaves as Products of Self-mixing Events: a Study of Open-system Processes in the Maua Granite, Sao Paulo, Brazil, Based on in situ Isotopic and Trace Elements in Plagioclase

Felsic microgranular enclaves with structures indicating that they interacted in a plastic state with their chemically similar host granite are abundant in the Maua Pluton, SE Brazil. Larger plagioclase xenocrysts are in textural disequilibrium with the enclave groundmass and show complex zoning patterns with partially resorbed An-rich cores (locally with patchy textures) surrounded by more sodic rims. In situ laser ablation-(multi-collector) inductively coupled plasma mass spectrometry trace element and Sr isotopic analyses performed on the plagioclase xenocrysts indicate open-system crystallization; however, no evidence of derivation from more primitive basic melts is observed. The An-rich cores have more radiogenic initial Sr isotopic ratios that decrease towards the outermost part of the rims, which are in isotopic equilibrium with the matrix plagioclase. These profiles may have been produced by either (1) diffusional re-equilibration after rim crystallization from the enclave-forming magma, as indicated by relatively short calculated residence times, or (2) episodic contamination with a decrease of the contaminant ratio proportional to the extent to which the country rocks were isolated by the crystallization front. Profiles of trace elements with high diffusion coefficients would require unrealistically long residence times, and can be modeled in terms of fractional crystallization. A combination of trace element and Sr isotope data suggests that the felsic microgranular enclaves from the Maua Pluton are the products of interaction between end-member magmas that had similar compositions, thus recording `self-mixing` events.

Menezesite, the first natural heteropolyniobate, from Cajati, Sao Paulo, Brazil: Description and crystal structure

Menezesite, ideally Ba2MgZr4(BaNb12O42)center dot 12H(2)O, occurs as a vug mineral in the contact zone between dolomite carbonatite and ""jacupirangite"" (=a pyroxenite) at the Jacupiranga mine, in Cajati county, Sao Paulo state, Brazil, associated with dolomite, calcite, magnetite, clinohumite, phlogopite, ancylite-(Ce), strontianite, pyrite, and tochilinite. This is also the type locality for quintinite-2H. The mineral forms rhombododecahedra up to I mm, isolated or in aggregates. Menezesite is transparent and displays a vitreous luster; it is reddish brown with a white streak. It is non-fluorescent. Mohs hardness is about 4. Calculated density derived from the empirical formula is 4.181 g/cm(3). It is isotropic, 1.93(1) (white light); n(calc) = 2.034. Menezesite exhibits weak anomalous birefringence. The empirical formula is (Ba1.47K0.53Ca0.3,Ce0.17Nd0.10Na0.06La0.02)(Sigma 2.66)(Mg0.94Mn0.23Fe0.23Al0.03)(Sigma 1.43)(Zr2.75Ti0.96Th0.29)(Sigma 4.00)[(Ba0.72Th0.26U0.02)(Sigma 1.00)(Nb9.23Ti2.29Ta0.36Si0.12)Sigma O-12.00(42)]center dot 12H(2)O. The mineral is cubic, space group 10 (204), a = 13.017(1) angstrom, V = 2206(1) angstrom(3), Z = 2. Menezesite is isostructural with the synthetic compound Mg-7[MgW12O42](OH)(4)center dot 8H(2)O. The mineral was named in honor of Luiz Alberto Dias Menezes Filho (born 1950), mining engineer, mineral collector and merchant. Both the description and the name were approved by the CNMMN-IMA (Nomenclature Proposal 2005-023). Menezesite is the first natural heteropolyniobate. Heteropolyanions have been employed in a range of applications that include virus-binding inorganic drugs (including the AIDs virus), homogeneous and heterogeneous catalysts, electro-optic and electrochromic materials, metal and protein binding, and as building blocks for nanostructuring of materials.

Global perturbation of the marine Ca isotopic composition in the aftermath of the Marinoan global glaciation

Ca isotopic compositions of Marinoan post-glacial carbonate successions in Brazil and NW Canada were measured Both basal dolostones display delta(44/40)Ca values between 1 and 0 7 parts per thousand overlying limestones show a negative Ca isotope excursion to values around 0 1 parts per thousand and delta(44/40)Ca values rapidly increase up-section to near 2 0 parts per thousand In the Brazilian successions those high delta(44/40)Ca values rapidly decrease and stabilize to values between 0 6 and 0 9 parts per thousand These Ca isotope secular variation trends are unlike those of Sturtian post-glacial carbonate successions but similar to those of Marinoan post-glacial carbonate successions in Namibia suggesting that the perturbation of the marine Ca cycle was global This recommends Ca isotope stratigraphy as a tool to correlate Neoproterozoic post-glacial carbonate successions worldwide While the lowermost and uppermost strata have delta(44/40)Ca values typical of Phanerozoic carbonates the extremes 0 1 and 2 0 parts per thousand have not been thus far reported for other marine carbonates These extreme values suggest a short-lived non-actualistic perturbation in the marine Ca cycle Simple box modelling of the Marinoan post-glacial marine Ca cycle can reproduce the extreme values only by postulating a two-step process with Ca input initially exceeding Ca removal trough carbonate precipitation followed by precipitation overtaking a decreased Ca Input (C) 2010 Elsevier B V All rights reserved

Cascades of Hopf bifurcations from boundary delay

We consider a 1-dimensional reaction-diffusion equation with nonlinear boundary conditions of logistic type with delay. We deal with non-negative solutions and analyze the stability behavior of its unique positive equilibrium solution, which is given by the constant function u equivalent to 1. We show that if the delay is small, this equilibrium solution is asymptotically stable, similar as in the case without delay. We also show that, as the delay goes to infinity, this equilibrium becomes unstable and undergoes a cascade of Hopf bifurcations. The structure of this cascade will depend on the parameters appearing in the equation. This equation shows some dynamical behavior that differs from the case where the nonlinearity with delay is in the interior of the domain. (C) 2009 Elsevier Inc. All rights reserved.

Reaction-diffusion systems coupled at the boundary and the Morse-Smale property

We study an one-dimensional nonlinear reaction-diffusion system coupled on the boundary. Such system comes from modeling problems of temperature distribution on two bars of same length, jointed together, with different diffusion coefficients. We prove the transversality property of unstable and stable manifolds assuming all equilibrium points are hyperbolic. To this end, we write the system as an equation with noncontinuous diffusion coefficient. We then study the nonincreasing property of the number of zeros of a linearized nonautonomous equation as well as the Sturm-Liouville properties of the solutions of a linear elliptic problem. (C) 2008 Elsevier Inc. All rights reserved.

NATURAL TOPOLOGIES ON COLOMBEAU ALGEBRAS

We define intrinsic, natural and metrizable topologies T(Omega), T, T(s,Omega) and T(s) in G(Omega), (K) over bar, G(s)(Omega) and (K) over bar (s) respectively. The topology T(Omega) induces T, T(s,Omega) and T(s). The topologies T(s,Omega) and T(s) coincide with the Scarpalezos sharp topologies.