Nonlinear partial differential equations (PDEs) characterise a wide range of complex phenomena in science and engineering, from fluid dynamics to signal processing in biomedical systems. In recent ...

Nonlinear partial differential equations (PDEs) are mathematical models that describe various phenomena in physics, engineering, and other fields. These equations can exhibit complex behaviors ...

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 ...

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: ...

Based at the University of Texas at Austin, Caffarelli started work on partial differential equations (PDEs) in the late 1970s and has contributed to hundreds of papers since.