Numerical approximations of non-local parabolic equations based on stochastic and finite elements methods and applications.

Abstract

Non-local equations in time arise in several applications, especially for modeling anomalous diffusion. In this context, it is very rare to have explicit solutions to the equations governing an anomalous diffusive phenomenon. However, numerical methods and stochastic representation can provide suitable approximations. The aim of this project is to determine whether stochastic representations and numerical approximations can be used in this context, and to compare the two approaches, whenever possible.

General Info

A co-tutorship between Torino and Pau, in the framework of UNITA- Universitas Montium, will be formalized for this project aiming to release of the double title between the two universities.

This PhD project is part of a call for 5 fully funded PhD scholarships in the framework of the PhD in Modeling and Data Science https://dottorato-mds.campusnet.unito.it/do/home.pl at the University of Turin (Italy). The call will open on 28 April 2022 (date TBC). The scholarship is for three years, starting in October 2022.

The PhD program is interdisciplinary, and it involves branches of mathematics, informatics, economics, statistics, and physics.

All interested candidates should submit their application online via the link https://www.phd.unito.it/do/home.pl/View?doc=Submitting_your_application.html. Deadline for applying is 30 May 2022 (date TBC). Notice that the application requires two reference letters, which should be submitted via the same link by the referees before the application deadline. The referees will be able to submit their letters only after the candidate has input all the required information and closed their (part of the) application. If the letters are not submitted by the deadline the application will not be valid.

For more information, do not hesitate to contact the supervisor. More information, including the official call and all relevant (confirmed) deadlines, can also be found here https://dottorato-mds.campusnet.unito.it/do/home.pl/View?doc=/content/Admission.html.

The call for applications is available at the page https://www.dottorato.unito.it/do/home.pl/View?doc=Bando_XXXVIII_ciclo.html. 

Admission details and the list of projects can be found here https://www.dottorato.unito.it/do/documenti.pl/ShowFile?_id=g3ot;field=file;key=JbqgKqg0lroYaYMa8BXEFYBVz1z8MXSdAKr7fGFtPR2;t=3298.