José Luiz Boldrini

Drug kinetics and drug resistance in optimal chemotherapy

A system of differential equations for the control of tumor cells growth in a cycle nonspecific chemotherapy is presented. First-order drug kinetics and drug resistance are taken into account in a class of optimal control problems. The results show that the strategy corresponding to the maximum rate of drug injection is optimal for the Malthusian model of cell growth (which is a relatively good model for the initial phase of tumor growth). For more general models of cell growth, this strategy proved to be suboptimal under certain conditions.

Fitting The Incidence Data From The City Of Campinas, Brazil, Based On Dengue Transmission Modellings Considering Time-dependent Entomological Parameters

Four time-dependent dengue transmission models are considered in order to fit the incidence data from the City of Campinas, Brazil, recorded from October 1st 1995 to September 30th 2012. The entomological parameters are allowed to depend on temperature and precipitation, while the carrying capacity and the hatching of eggs depend only on precipitation. The whole period of incidence of dengue is split into four periods, due to the fact that the model is formulated considering the circulation of only one serotype. Dengue transmission parameters from human to mosquito and mosquito to human are fitted for each one of the periods. The time varying partial and overall effective reproduction numbers are obtained to explain the incidence of dengue provided by the models.

Some Controllability Results for Linear Viscoelastic Fluids

We analyze the controllability properties of systems which provide a description, at first approximation, of a kind of viscoelastic fluid. We consider linear Maxwell fluids. First, we establish the large time approximate-finite dimensional controllability of the system, with distributed or boundary controls supported by arbitrary small sets. Then, we prove the large time exact controllability of fluids of the same kind with controls supported by suitable large sets. The proofs of these results rely on classical arguments. In particular, the approximate controllability result is implied by appropriate unique continuation properties, while exact controllability is a consequence of observability (inverse) inequalities. We also discuss questions concerning the controllability of viscoelastic fluids and some related open problems.

An error estimate uniform in time for spectral semi-Galerkin approximations of the nonhomogeneous Navier-Stokes equations

We consider the spectral semi-Galerkin method applied to the non-homogeneous Navier-Stokes equations, which describes the motion of miscibles fluids. Under certain conditions it is known that the aproximate solutions constructed by using this method converge to a global strong solution of these equations. In this paper we prove that these solutions satisfy an optimal uniform in time error estimate in the H 1-norm for the velocity. We also derive an uniform error estimate in the L ∞-norm for the density and an improved error estimate in the L 2-norm for the velocity.

Abiotic Effects on Population Dynamics of Mosquitoes and Their Influence on Dengue Transmission

Dengue incidence is dependent on abiotic factors that directly affect the population dynamics of mosquitoes with serious implications for dengue transmission. By using estimated entomological parameters dependent on temperature, and including the dependency of these parameters on rainfall, the seasonally varying population size of the mosquito Aedes aegypti is evaluated using a mathematical model. The anthropophilic and peridomestic female A. aegypti bite humans for blood to mature fertilised eggs, during which the dengue virus can spread between mosquitoes and humans. As an example of applied entomology, mosquito and human populations are coupled to assess dengue virus transmission. Seasonal patterns of mosquito populations influence dengue epidemics, illustrating the importance of temperature and rainfall in designing control mechanisms.

A note on immersions of domains of fractional powers of certain sectorial operators in Sobolev spaces

Abstract In this note we give a proof of a result on immersions of domains of fractional powers of certain sectorial operators associated to strongly elliptic operators in Sobolev spaces; such immersions preserve information on fractional derivatives. We also briefly comment on the application of this result to a problem of optimal control of mosquito populations.

Error Estimates for Full Discretization of a Model for Ostwald Ripening

We analyze certain finite element schemes for a family of systems consisting of a Cahn–Hilliard equation coupled with several Allen–Cahn type equations, which are related to a model proposed by Fan and Chen for the evolution of Ostwald ripening in two-phase material systems. We obtain error bounds both for a semidiscrete (in time) scheme and a fully discrete scheme.

Periodic motions of sucker rod pumping systems

AMONG the most important of the artificial lifting methods used in petroleum industries are the sucker rod pumping systems. In order to improve the design and the operation of such installations, it is necessary to understand their behavior, especially at infield situations. The pumping system is put into action by an engine that imparts a periodic motion to the top of the rods, and eventually all of the system sets itself in a periodic motion. To describe this behavior, several mathematical models have been developed over the years by taking into consideration various inertial and dissipation effects in the system, material properties, down hole pumping conditions, fluid interactions, and so on (see for instance Doty and Schmidt [l]). Obviously, several nonlinearities are present in the problem, but there is one that is intrinsic to the pumping system itself. This is due to the presence of the valve mechanism that imposes sudden changes in the stress acting on the rods according to the opening or the closing of the down hole and walking valves. Concerning the study of these models, some theoretical analysis has been done in certain linearized versions of the models, and many numerical experiments were performed. In general, however, there is a lack of sound mathematical analysis of the nonlinear models. In this paper we consider a simple model that takes into consideration the elastic response of the rods, the dissipation mechanism (due to internal material dissipation and hydraulic friction) and the stress change due to the valve mechanism. It corresponds to the same partial differential equation used in Pavlik and Schafer [2], it is a wave equation with dissipation, but with a nonlinear and discontinuous boundary condition modeling the action of the valves. Our objective is to study the interaction between the action of the valves with the periodic motion imparted by the engine on the top of the rods in the production of the final motion of the rod. We are able to show the existence of a strong forced periodic solution for the mathematical model of this problem in the following way: we first show that the operator associated to the problem is maximal monotone in a convenient Hilbert space. Thus, we are in the setting of the well-known theory of monotone operators, but we cannot apply its standard results on periodic solutions because our operator is neither strictly monotone nor coercive. The main difficulty is to control the influence of the boundary conditions. We then proceed by approximating our equation in a suitable way by equations for which the corresponding operators are strictly coercive; for them the standard theory can be applied, and approximated periodic solutions are obtained. We then strive to obtain certain estimates for these approximated solutions, which permit us to conclude that they approach a mild periodic solution of the original problem. An essential step for this is the construction of an adequate Liapunov function that furnishes an

Phase Field: A Methodology to Model Complex Material Behavior

This work was done in commemoration of the 50th anniversary of the inauguration of the Institute of Mathematics, Statistics and Scientific Computation of the University of Campinas, Brazil (Instituto de Matematica, Estatistica e Computacao Cientifica da Universidade Estadual de Campinas). Our objective is just to give a rather fast introduction to some important modeling aspects of the phase field approach to model complex material behavior; we aim at students of mathematics who have almost no previous background in continuum thermomechanics. Thus, we briefly recall some of its main concepts and explain the main approaches used to derive the governing equations including the phase field variables (diffusification, energetic variational, and entropy approaches); we comment on some of their limitations and relationships, and briefly describe a few simple applications.

A mathematical model for thermoregulation in endotherms including heat transport by blood flow and thermal feedback control mechanisms: changes in coat, metabolic rate, blood fluxes, ventilation and sweating rates

ABSTRACT Thermoregulation in endotherms allows the maintenance of the body temperature independent of ambient temperature. Experimental data have revealed complex interactions between the physiological mechanisms of thermoregulation and environmental conditions. We derive a nonlinear partial integro-differential dynamical model based on physical first principles and fundamental physiological mechanisms to understand the role of some thermal control mechanisms in the thermoregulation process of endotherms. The model is composed of four layers representing different tissues and it incorporates six thermal feedback control mechanisms. These mechanisms are heat production due to metabolic rate and heat exchange within the body given its internal structure, and the model considers heat exchange due to conduction, heat transport by blood flow, heat exchange with the ambient through convection, radiation, and evaporation from the respiratory tract and superficial evaporation in both passive and active situations. Our model sheds new light on previous explanations about the classic metabolism-ambient temperature U-shaped curve.