Boundary value problems for nonlinear partial differential equations form a cornerstone of modern mathematical analysis, bridging theoretical advancements and practical real-world applications. These ...

An advanced course in the analytical and numerical study of ordinary and partial differential equations, building on techniques developed in Differential Equations I. Ordinary differential equations: ...

We consider a specific type of nonlinear partial differential equation (PDE) that appears in mathematical finance as the result of solving some optimization problems. We review some examples of such ...

Sometimes, it’s easy for a computer to predict the future. Simple phenomena, such as how sap flows down a tree trunk, are straightforward and can be captured in a few lines of code using what ...

Luis Caffarelli has won the 2023 Abel prize, unofficially called the Nobel prize for mathematics, for his work on a class of equations that describe many real-world physical systems, from melting ice ...

Mathematicians finally understand the behavior of an important class of differential equations that describe everything from water pressure to oxygen levels in human tissues.

We discuss two Newton-like methods for solving the systems which arise from nonlinear partial differential equations and nonlinear networks. Under appropriate conditions both methods provide global ...

Journal of Nonlinear Waves is the home for the field of nonlinear wave phenomena, broadly defined. It publishes authoritative articles on theoretical and computational aspects of nonlinear waves ...

This book serves as a bridge between graduate textbooks and research articles in the area of nonlinear elliptic partial differential equations. Whereas graduate textbooks present basic concepts, the ...