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.