Nonlinear elliptic and parabolic partial differential equations (PDEs) constitute a cornerstone of modern analysis, modelling a wide variety of steady-state and time-evolution phenomena in physics, ...

We consider the Heston model as an example of a parameterized parabolic partial differential equation. A space-time variational formulation is derived that allows for parameters in the coefficients ...

Controllability of parabolic partial differential equations concerns the capacity to guide the evolution of diffusion-type systems—such as heat flow or chemical concentration—towards a desired state ...

Partial differential equations (PDEs) lie at the heart of many different fields of Mathematics and Physics: Complex Analysis, Minimal Surfaces, Kähler and Einstein Geometry, Geometric Flows, ...

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: ...

Two new approaches allow deep neural networks to solve entire families of partial differential equations, making it easier to model complicated systems and to do so orders of magnitude faster. In high ...