Introduction to Partial Differential Equations.

Introduction to stochastic partial differential equations

We introduce the Hilbert space-valued Wiener process and the corresponding stochastic integral of Itô type. This is then used together with semigroup theory to obtain existence and uniqueness of weak solutions of linear and semilinear stochastic evolution problems in Hilbert space. Finally, this abstract theory is applied to the linear heat and wave equations driven by additive noise.

Partial Differential Equations applied to Medical Image ‎Segmentation

‎This paper presents an application of partial differential equations(PDEs) for the segmentation of abdominal and thoracic aortic in CTA datasets. An important challenge in reliably detecting aortic is the need to overcome problems associated with intensity inhomogeneities. Level sets are part of an important class of methods that utilize partial differential equations (PDEs) and have been exte...

An Introduction to the Controllability of Partial Differential Equations

These notes are a written abridged version of a course that both authors have delivered in the last five years in a number of schools and doctoral programs. Our main goal is to introduce some of the main results and tools of the modern theory of controllability of Partial Differential Equations (PDE). The notes are by no means complete. We focus on the most elementary material by making a parti...

Introduction to Variational Methods in Partial Differential Equations and Applications

Introduction to Differential Equations