María Eugenia Martínez Martini

Welcome to my homepage

I obtained PhD last November at the Department of Mathematical Engineering (DIM) of the University of Chile, under the advise of Prof. Claudio Muñoz. I obtained my B.Sc. in Mathematics degree at the National University of Río Cuarto.

Contact information: maria.martinez.m@uchile.cl

My research interest

I am interested in dispersive PDEs, more specifically, Schrödinger type ecuations and water waves models, such as Zakharov system, Davey-Stewartson, Zakharov-Rubenschik/Benney-Roskes. For these models, I study long-time behavior of solutions, decay properties, solitons and collisions.

Publications

On the behavior of solitary waves for the Whitham equation in a slowly varying medium (with Frédéric Rousset) under preparation.
Existence of solitary waves in the Water Waves Zakharov system with slowly varying bottom. Part 2. (with Frédéric Rousset) under preparation.
Existence of solitary waves in the Water Waves Zakharov system with slowly varying bottom. Part 1. (with Frédéric Rousset), part of my Ph.D thesis (Chapter 5).
On the long-time behavoir of solutions to the ZR/BR equation (with José Manuel Palacios), in the arXiv link
On the decay problem for the Zakharov and Klein-Gordon Zakharov systems in one dimension, in the arXiv link.
Decay of small odd solutions of long range Schrödinger and Hartree equations in one dimensión. Nonlinearity 33 (2020), pp. 1156–1182.

Teaching experience

As an assistant professor in the Unversity of Chile

In the courses: Topics in Dispersive PDEs, Topology and Functional Analysis, Honors Partial Differential Equations, Linear Algebra.

As a professor in the University San Sebastián

In the courses: Analytic Geometry, Calculus I.

As an assistant professor in the National University of Río Cuarto

In the course: Linear Algebra.

Recent talks

Primer encuentro virtual de jóvenes investigadores: "proyectando el futuro de la investigación", at the USACH. September 2020.
Workshop Nonlinear Dispersive Equations, organized by IMPA. Florianópolis, Santa Catarina, Brasil. September 2020.
SUMA, organized by UMA and Somachi. Mendoza, Argentina. September 2019.
Nonlinear dispersive waves, solitons, and related topics, at the Mittag-Leffler Institute. Stochholm Sweden. June 2019.

Visits

Université Paris-Saclay, France, with Professor Frédéric Rousset. November-December 2019.
Universidad de Granada, Spain, with Professor Juan Soler. June-July 2019.
Université Paris-Saclay, France with Professor Frédéric Rousset. May-June 2019.

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