# NPDE Lecture 1 Discussion

I am going to start a series of lectures on nonlinear partial differential equations. Advancements made in the theory of nonlinear PDEs is one of the main achievements in XX century mathematics. Let me first make a remark on linear PDEs. In some sense one can say that there is a complete theory of linear PDEs, and perhaps the best source would be the four volumes of “The Analysis of Linear Partial Differential Operators” by Lars Hörmander [3]. The importance of the nonlinear PDEs is associated with the fact that they reflect more precise nonlinear laws of the nature, while linear PDEs were derived from the linearized versions of the nonlinear laws. Despite the great advances in the theory of nonlinear PDEs it is far from being complete. It is remarkable that almost every major nonlinear PDE has its own personality and requires unique approach. However, looking to current state of art in the theory of nonlinear PDEs, one can observe a similarity with the classical linear theory in the following sense: there are some major individual nonlinear PDEs, and analysis and understanding of those PDEs is a key towards the general theory of a broad class of nonlinear PDEs. I am going to concentrate on one of those key nonlinear PDEs called the nonlinear diffusion equation, which is a generalization of the classical heat/diffusion equation. adidas femme Continue reading NPDE Lecture 1 Discussion

# Welcome to Ugur Abdulla’s Mathematical Blog

National Science Foundation funded Research Experience for Undergraduates Site on Partial Differential Equations and Dynamical Systems has been successfully established at Florida Institute of Technology. Buy Blade and Soul Gold In the first summer session in 2014 10 undergraduate students representing University of Chicago, City University of New York, University of Michigan, Williams College, University of Illinois at Urbana-Champaign, University of Auburn, University of Pennsylvania, California State University at Long Beach, University of Redlands and Florida Institute of Technology pursued research under my supervision. Adidas Superstar Students worked in there groups working on Nonlinear Partial Differential Equations, Optimal Control and Inverse Problems and Dynamical Systems and Chaos Theory. All 10 students are selected as presenters in YMC-2014 in Ohio State University, August 22-24, 2014. fjallraven kanken classic Here is the link to abstracts of all three presentations. adidas messi Analysis of Interfaces for the Nonlinear Diffusion Equation with Linear Convection by Taylor P Schluter & Lauren T Lanier & Kev Johnson On the Structure of Minimal $4(2k+1)$-orbits of Continuous Endomorphisms and Universality in Chaos by Rashad U Abdulla & Batul Kanawati & Anders Ruden On Some Inverse Free Boundary Problems for Second Order Parabolic PDEs by Nicholas Crispi & Daniel Kassler & Paige Williams & Bruno Poggi & Scott Pelton-Stroud Attached youtube video features final presentations by students at the end of the summer session of 2014.