On some evolution differential equations

Faculty-development competitive research grants program for 2023-2025

The evolution differential equations have backgrounds in several areas like Physics, Chemistry, engineering, etc. When faced with a specific evolution equations that has emerged from the modelling process, an important part of the mathematical analysis is to establish that the problem has been correctly formulated. Almost all equations appearing in the area of partial differential equations present models in other sciences.
In this project, we propose some evolution models and study them from the mathematical point of view with the hope of providing some useful insights to the other science communities. More specifically, the goal of this project is to introduce early stage researchers at the masters, PhD, and postdoctoral level to the modern analytical techniques used in the study of hyperbolic and parabolic partial differential equations, and use these techniques to study the qualitative and quantitative properties of the corresponding physical systems.

It is expected that at least three publications will be produced as a result of this project, and they are also presented in international prestigious Conferences. Although these results are intended for an audience of mathematicians, they may also be of use to researchers studying the physical contexts since some aspects of our expected results may be fruitful in experimental researches. From the pedagogical perspective, the results of this project train future researchers in analytical techniques used in mathematical modelling.