# Jean Carlos NakasatoUniversity of São Paulo | USP

Jean Carlos Nakasato

## About

17

Publications

1,743

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32

Citations

Citations since 2017

Introduction

Additional affiliations

June 2020 - May 2021

## Publications

Publications (17)

In this paper we consider the homogenization of the evolution problem associated with a jump process that involves three different smooth kernels that govern the jumps to/from different parts of the domain. We assume that the spacial domain is divided into a sequence of two subdomains An∪Bn and we have three different smooth kernels, one that contr...

In this paper we study an abstract framework for computing shape derivatives of functionals subject to PDE constraints in Banach spaces. We revisit the Lagrangian approach using the implicit function theorem in an abstract setting tailored for applications to shape optimization. This abstract framework yields practical formulae to compute the deriv...

In this work we analyze the asymptotic behavior of the solutions of the p-Laplacian equation with homogeneous Neumann boundary conditions set in bounded thin domains as R ε = (x, y) ∈ R 2 : x ∈ (0, 1) and 0 < y < εG (x, x/ε^α), α>0. We take a smooth function G : (0, 1) × R → R, L-periodic in the second variable, which allows us to consider locally...

In this paper we analyze the asymptotic behaviour of a control problem set by a convection-reaction-diffusion equation with mixed boundary conditions and defined in a tubular thin domain with rough boundary. The control term acts on a subset of the rough boundary where a Robin-type boundary condition and a catalyzed reaction mechanism are set. The...

In this paper we study the asymptotic behavior of the solutions of a class of nonlinear elliptic problems posed in a 2-dimensional domain that degenerates into a line segment (a thin domain) when a positive parameter $\varepsilon$ goes to zero. We also allow high oscillating behavior on the upper boundary of the thin domain as $\varepsilon \to 0$....

In this paper, we study a reaction–diﬀusion problem in a thin domain with varying order of thickness. Motivated by the applications, we assume the oscillating behavior of the boundary and prescribe the Robin-type boundary condition simulating the reaction catalyzed by the upper wall. Using the appropriate functional setting and the unfolding operat...

In this work we analyze the asymptotic behavior of the solutions of the p-Laplacian equation with homogeneous Neumann boundary conditions set in bounded thin domains as R ε = (x, y) ∈ R 2 : x ∈ (0, 1) and 0 < y < εG (x, x/ε). We take a smooth function G : (0, 1) × R → R, L-periodic in the second variable, which allows us to consider locally periodi...

In this work we apply the unfolding operator method to analyze the asymptotic behavior of the solutions of the $p$-Laplacian equation with Neumann boundary condition set in bounded thin domains of the type $R^\varepsilon=\left\lbrace(x,y)\in\mathbb{R}^2:x\in(0,1)\mbox{ and }0<y<\varepsilon g\left({x}/{\varepsilon^\alpha}\right)\right\rbrace$. We ta...

In this paper we study an abstract framework for computing shape derivatives of functionals subject to PDE constraints. We revisit the Lagrangian approach using the implicit function theorem in an abstract setting tailored for applications to shape optimization. This abstract framework yields practical formulae to compute the derivative of a shape...

In this paper we consider the homogenization of the evolution problem associated with a jump process that involves three different smooth kernels that govern the jumps to/from different parts of the domain. We assume that the spacial domain is divided into a sequence of two subdomains $A_n \cup B_n$ and we have three different smooth kernels, one t...

In this paper we consider the homogenization problem for a nonlocal equation that involve different smooth kernels. We assume that the spacial domain is divided into a sequence of two subdomains $A_n \cup B_n$ and we have three different smooth kernels, one that controls the jumps from $A_n$ to $A_n$, a second one that controls the jumps from $B_n$...

In this work we use reiterated homogenization and unfolding operator approach to study the asymptotic behavior of the solutions of the p-Laplacian equation with Neumann boundary conditions set in a rough thin domain with concentrated terms on the boundary.
We study weak, resonant and high roughness, respectively. In the three cases, we deduce the...

In this work we use reiterated homogenization and unfolding operator approach to study the asymptotic behavior of the solutions of the $p$-Laplacian equation with Neumann boundary conditions set in a rough thin domain with concentrated terms on the boundary. We study weak, resonant and high roughness, respectively. In the three cases, we deduce the...

In this work we analyze the solutions of a $p$-Laplacian equation with homogeneous Neumann boundary conditions set in a family of rough domains with a nonlinear term concentrated on the boundary. At the limit, we get a nonlinear boundary condition capturing the oscillatory geometry of the strip where the reactions take place.

In this work we analyze the solutions of a p-Laplacian equation with homogeneous Neumann boundary conditions set in a family of rough domains with a nonlinear term concentrated on the boundary. At the limit, we get a nonlinear boundary condition capturing the oscillatory geometry of the strip where the reactions take place.

In this paper, we investigate a convection–diffusion–reaction problem in a thin domain endowed with the Robin-type boundary condition describing the reaction catalyzed by the upper wall. Motivated by the microfluidic applications, we allow the oscillating behavior of the upper boundary and analyze the resonant case where the amplitude and period of...

## Projects

Project (1)

We analyze the behavior of the solutions of PDEs when their domain of definition is perturbed. Following the approach introduced by D. Henry, we consider regular perturbations of the boundary for boundary value problems, that means, the perturbation of the domain is established by smooth diffeomorphisms. But we also can study more general situations, called singulars, such as thin domain problems and perforated ones (according to J. Hale and G. Raugel, and D. Cioranescu and F. Murat respectively).