We study the classical linear partial differential equations: Poisson's equation and the heat equation. We learn about representation formulas for solutions, maximum principles, and energy estimates.

This monograph offers a comprehensive exposition of the theory surrounding time-fractional partial differential equations, featuring recent advancements in fundamental techniques and results. The ...

The Saint Venant equations are two nonlinear partial differential equations (PDE) which are used to describe the dynamics of one-dimensional flow in open water channels. Despite being nonlinear PDEs, ...

However, the high-dimensional complexity of spatiotemporal phenomena makes these models difficult to interpret. This paper proposes a river network feature identification architecture based on coupled ...

Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential ...

Introduction to analytical and numerical methods for finding solutions to differential equations involving two or more independent variables. Topics include linear partial differential equations, ...

A collection of resources regarding the interplay between differential equations, deep learning, dynamical systems, control and numerical methods.

The course provides an introduction to the theoretical basis for linear partial differential equations, focusing on elliptic equations and eigenvalue problems. The techniques and methods developed are ...

This course focuses on first and second-order partial differential equations, with examples and applications from selected fields such as physics, engineering and biology. Topics may include the wave ...