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

This is a preview. Log in through your library . Abstract The explosion probability before time t of a branching diffusion satisfies a nonlinear parabolic partial differential equation. This equation, ...

Partial differential equations are ubiquitous in almost all applications of mathematics, where they provide a natural mathematical description of many phenomena involving change in physical, chemical, ...

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 ...

Nonlinear waves; integrable systems; solitons; mathematical modeling in social and behavioral science. The study of wave phenomena by means of mathematical models often leads to a certain class of ...

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 ...