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 ...

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

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 ...

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 ...

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 ...

Calculation: A representation of a network of electromagnetic waveguides (left) being used to solve Dirichlet boundary value problems. The coloured diagrams at right represent the normalized ...

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 ...

Studies properties and solutions of partial differential equations. Covers methods of characteristics, well-posedness, wave, heat and Laplace equations, Green's functions, and related integral ...

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 ...