Well-posedness for a class of nonlinear degenerate parabolic equations

In this paper we obtain well-posedness for a class of semilinear weakly degenerate reaction-diffusion systems with Robin boundary conditions. This result is obtained through a Gagliardo-Nirenberg interpolation inequality and some embedding results for weighted Sobolev spaces

Exact controllability for quasi-linear perturbations of KdV

We prove that the KdV equation on the circle remains exactly controllable in arbitrary time with localized control, for sufficiently small data, also in presence of quasi-linear perturbations, namely nonlinearities containing up to three space derivatives, having a Hamiltonian structure at the highest orders. We use a procedure of reduction to constant coefficients up to order zero, classical Ingham inequality and HUM method to prove the controllability of the linearized operator. Then we prove and apply a modified version of the Nash-Moser implicit function theorems by H\"ormander.Comment: 39 page

Multiplicative controllability for nonlinear degenerate parabolic equations between sign-changing states

In this paper we study the global approximate multiplicative controllability for nonlinear degenerate parabolic Cauchy problems. In particular, we consider a one-dimensional semilinear degenerate reaction-diffusion equation in divergence form governed via the coefficient of the \-reaction term (bilinear or multiplicative control). The above one-dimensional equation is degenerate since the diffusion coefficient is positive on the interior of the spatial domain and vanishes at the boundary points. Furthermore, two different kinds of degenerate diffusion coefficient are distinguished and studied in this paper: the weakly degenerate case, that is, if the reciprocal of the diffusion coefficient is summable, and the strongly degenerate case, that is, if that reciprocal isn't summable. In our main result we show that the above systems can be steered from an initial continuous state that admits a finite number of points of sign change to a target state with the same number of changes of sign in the same order. Our method uses a recent technique introduced for uniformly parabolic equations employing the shifting of the points of sign change by making use of a finite sequence of initial-value pure diffusion pro\-blems. Our interest in degenerate reaction-diffusion equations is motivated by the study of some \-energy balance models in climatology (see, e.g., the Budyko-Sellers model) and some models in population genetics (see, e.g., the Fleming-Viot model).Comment: arXiv admin note: text overlap with arXiv:1510.0420

Self-Test Mechanisms for Automotive Multi-Processor System-on-Chips

L'abstract è presente nell'allegato / the abstract is in the attachmen

TEACHING VOCABULARY BY USING PICTURES TO THE FIRST GRADE STUDENTS IN SDN DUWET 01 BAKI SUKOHARJO

ABSTRACT Linggar Floridia. 2013 .Teaching Vocabulary by Using Pictures to The First Grade Students In SDN Duwet 01 Baki Sukoharjo. English Diploma Program, Faculty of Letters and Fine Arts, Sebelas Maret University. This final project report was written based on the job training in SDN Duwet 01 Baki Sukoharjo on February 4th to April 2nd2013. The objectives of this report are to describe the process of teaching English vocabulary by using pictures for the first grade students of SDN Duwet 01, to find out the problems of teaching English vocabulary by using pictures and to provide the solution to the problems of teaching English vocabulary by using pictures. In the job training, I did some activities such as class observation and made a lesson plan. I use the pictures as media to teach the vocabulary to the students. The process of teaching vocabulary consists of building knowledge of the field, modeling of the text, joint construction, independent construction and closing. There were some problems in teaching vocabulary by using pictures to the first grade students in SDN Duwet 01 Baki. The problems were the size of pictures, the difficulty in pronouncing and memorizing English words, and the lack of teaching materials. The solution to solve the problems were giving clear pictures, telling the instruction of the way to answer relate to the pictures and bringing some pictures related to the topic. From the discussion in this final project, the readers would know that using picture is necessary and effective for teaching vocabularies especially to the first grade students of SDN Duwet 01 Baki Sukoharjo

Concepts and Experiences: The Theoretical Pragmatism of Luigi Bobbio

For Symposium abstract is not require

Well-posedness of 2D and 3D swimming models in incompressible fluids governed by Navier--Stokes equations

We introduce and investigate the wellposedness of two models describing the self-propelled motion of a "small bio-mimetic swimmer" in the 2D and 3D incompressible fluids modeled by the Navier-Stokes equations. It is assumed that the swimmer's body consists of finitely many subsequently connected parts, identified with the fluid they occupy, linked by the rotational and elastic forces. The swimmer employs the change of its shape, inflicted by respective explicit internal forces, as the means for self-propulsion in a surrounding medium. Similar models were previously investigated in [15]-[19] where the fluid was modeled by the liner nonstationary Stokes equations. Such models are of interest in biological and engineering applications dealing with the study and design of propulsion systems in fluids and air.Comment: 28 pages, 5 figures, Corresponding author: Alexandre Khapalov, Department of Mathematics, Washington State University, USA (email: [email protected]

Nonnegative controllability for a class of nonlinear degenerate parabolic equations with application to climate science

Let us consider a nonlinear degenerate reaction-diffusion equation with application to climate science. After proving that the solution remains nonnegative at any time, when the initial state is nonnegative, we prove the approximate controllability between nonnegative states at any time via multiplicative controls, that is, using as control the reaction coefficient.Comment: arXiv admin note: text overlap with arXiv:1710.0069

Nonnegative multiplicative controllability for semilinear multidimensional reaction-diffusion equations

We consider a multidimensional semilinear reaction-diffusion equation and we obtain at any arbitrary time an approximate controllability result between nonnegative states using as control term the reaction coefficient, that is, via multiplicative controls