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 ...

Recent decades have witnessed a bloom in research at the interface of complex geometry and nonlinear partial differential equations. This interdisciplinary field explores the deep and intricate ...

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 ...

We show that any entire solution of an essentially nonlinear first-order partial differential equation in two variables must be linear. Journal Information This monthly journal, begun in 1950, is ...

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 ...

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, ...

Governing equations in the form of ordinary and partial differential equations are valuable models for physical systems. However they can be difficult to derive, making them unknown, particularly for ...

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, ...

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 ...

We derive a partial differential equation (PDE) representation for the value of financial derivatives with bilateral counterparty risk and funding costs. The model is very general in that the funding ...